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number series, COMBINATION SERIES, finally how to deal with a series given…
number series
COMBINATION SERIES
fraction series(14)
so when a series is continuously increasing and decresing one digit after another it means it belong to alternate series
sometimes if it may not be continous also but by seeing alternate digits in series if have any relation we may say it as alternate series
coming to fraction series, this series have a different kind of graph like listed
with the different graph as above along with it if the operation is multiplication then we can say it is fraction series
and when you realised certain series is a fraction series then you need to do multiplication in series not in direct multiples
because since it is a fraction series here the underlying pattern will be definitely multiplication with some decimals(nothing but fraction)
sometimes just above will give us next digit and someother times we need to add or sub some numb from the calcu we got above inorder to get next numb
square series(12)
this is not direct square series, and in both square series and cube series complex numb concept is involved
how to ans them case1:
here he will a series and each numb in series is nearer to some square number
0, 3, 8, 15, 24, ?
if you look ate whole series they are not direct squares but they are nearer to squares
step 1: write the nearest square to given numb in series
1,4,9,16, 25
step2: now subtract as original squares - nearer squares given in series
1-0= 1
9-8 = 1
16-15=1
4-3 =1
make a note here we did original square - series only follow same pattern for every problem
25-24=1
by the end of this step 2 we will be knowing the pattern
1 is our pattern
case2:
here also he will givr nearer square series and asks us to fing next numb in the series
in above case we consedered original squares and did subtraction and got a regular pattern, but in this case when we consider original squares and squares in series and subtract them the pattern we get is very irregular
if like this we got irregular pattern in square series now wehave to deal them in different way, using difference that is by calculating diff
example: 1,2,6,15,31
step1: usually consider original squares and try to calculate pattern
1,2,6,15,31
4,916,25,36
now pattern calculation
4-1= 3, 9-2=7, 16-6=10, 25-10=15, 36-31=5
3, 7,10,15,5 is our pattern which is very irregular and unable to predict next pattern
in such times we follow difference approach as below
step2: calculate diff b/w every 2 numbers in the series
2,6
6-2=4
6,15
15-6=9
1,2
2-1=1
15,31
31-15=16
if you look at above diff 1,4,9,16 there are in pattern nothing but squares
our next square is 25, now add this 25 to last digit to get next digit in the series
step3: 31+25 =56
56 is our next numb in series
here you can see patterns like
same above patten as minus
like 2^2-1, 2^2-2, 2^2-3, 2^2-4........
n^3 - n, n^3-n
means 8^3 -8, 7^3 -7, 6^3 -6,.......
n^2 +1, n^2+2, n^2+3, n^2+4.........
certain square + incrementing numb pattern
here square also keep on increasing or it can be same both are possible
like 2^2+1, 2^2+2, 2^2+3, 2^2+4........
3^2+2, 3^2+2, 3^2+3, 3^2+3........
alternate series(8)
here he will give us series which is increasing and decreasing continuously, increasing / decreasing
case1: when an increasing series is given it is difficult for us to quickly recognize it as atlernater series, because if nothing is familiar we first go for multiplication or maultiplication with diff, then fraction series then comes to atlernate series to check. so obviously it takes time
case2: when given decreasing series also it is difficult fot us as we 1st go for division, then division with diff, fraction series then comes to alternate series, this also takes time
case3: but when a series is given like increased numb, decreased numb, increaded numb , decreased numb we can identify easily
case1:
here increasing series is given which belongs to laternative series
ex: 8,11,14,17,20,23,?
how to solve them
step1: check if the series is familiar
case3
step1: when we recognize if given series is a alternate series first thing we need to do is seperate the series alternately
like which numb we need to find consider that numb alternate numbers and make it as a series
16, 18,20, ?
step 2: now find pattern in this series
+2 is our pattern
link to youtube.com
step3: calculate the next numb based on pattern
20 + 2 = 22
question: here he will give series like 15,16, 13, 18, 11, 20, 9,? means here our series is in continuous increse and decresing order
multiplication with subtraction series7()
this multiplication with subtraction series are in decreasing order with huge diff b/w each consecutive number in series(simply b/w 2 numb aside of one and another)
it could be
1 time or
2 times(of before numb) and subtraction of certain number gives next numb in the series
qsn
grouping logic series(9)
in grouping logic series we have specifically seen tripples pattern
here we have 3 num in a group
if we perform some operation to any 2 numbers we will get 3rd number
how to recognize grouping series
they are very irregular like series is rapid increment, normal inccrement, normal decrement, rapid decrement, normal increment it involves various kind of increments and decrements
in all the above series the length of the series is very less like he gives 5 numbs in series and asks us to find 6th numb
BUT in grouping series he will only give 8 numbers in the series(which is very ireegular) and asks us to find 9th numb
this is because here we need to divide whole series into groups and fing relation b/w each group
and each group should have atleast 3 numbers so obviously series will be lenghty
how to solve them
he will give question like 3,4,5,5,12,13,7,24,25,8,15,?
easy example: 4,6,24,15,12,180,14,25,?
step1: not familair
step2: dont belong to any other series
step3: diving into groups
4,6,24
here relation is 4* 6 = 24
15,12,180
15* 12 = 180
14,25,?
now 14 * 25
= 350
step4: our next numb in series is 350
setp 3: first divide whole series into groups and find relation b/w each group(each group should have 3 numbers)
5,12,13
similarly
25+ 144 = 169
means 5^2 + 12^2 = 13^2
7,24,25
3,4,5
on just eye view they may seem unfamiliarr but look at carefully
3^2 + 4^2 = 5^2
which means 9 + 16 =25
8,15
64 + 225
289
means 17^2
step1: check if whole series is familiar
step 2: look for multi or alternate series, fraction series if not then go with grouping logic series
step4: based on this relation find missing numb
multiplication and addition series(6)
if a series is in rapid increase with direct multiples it is known as multiplication series
but if a series is in direct multiplication along aith addition of certain number gives multiplication and addition series
binary series(11)
fabanacci series(10)
cube series(13)
finally how to deal with a series given
step1: analyze if given series is familiar or not
means check if the whole series are any squares, cubes, primes , composite, complex numbers
if yes
solve with their respected position
if not
go for step2
step2: check if they belong to another series
like fraction series, grouping logic series,binary series, square series, cube series, prime series, alternate series
if yes
solve accordingly
if not go for setp3
step3:
if series is rapidly increasing
check for direct multiplication
if the series is rapidly decreasing
check for direct division
step4:
for rapid increasing / decresing series only
check for multiplication or division with difference
step5: if all above didnt work then go for differences method
means taking difference b/w each 2 terms to know the pattern
step6: if all above didnt work go for digital operations
dont panic by seeing at all the procedure like this much lenghty ani, this is a formal procedure
but when you look at series you will get a idea and you will be struck at any two methods and in this 2 you need to chhose one based on the priority and solve the prolem
major note
iif familiar and pattern is irregular
check if pattern is combination of complex numb of not complex numb only go for mul
means whatever patern you have got if it is easily recognizable means ok, if not check for complex numb
if complex numb also didnt work means then go for next type
if multiples
pattern irregular
check if pattern is made of complex numb if not only go fot diff
for any series he gave if corresponding process dindt work means immediately go for diff
ex: he given alternate series but alternate series process is not giving us pattern even when we checked with complex numb means
for any series be it simlar squares, silimilar cubes, or any series if that particular process didnt work means go for diff
and mostly this kind of qsns are given for similar squres and similar cubes
like qsns seem like similar square or similar cube when we solve it accor to those process we didnt get pattern even after checking for complex numb
so we go for diff
if diff
pattern irregular
check for complex numb
types of series
division series
in division series we can see series in rapid decrease
qsn: here he will give a series which is rapidly decresing and asks us to find the next numb
ex: 162, 54, 18, 6, ?
solution process
here also we need to check for highest numb first
step1: find the relation b/w 1st 2 numb in series
162, 54
in 16 table where 50 goes
16
1 =16, 16
2= 32, 16
3=48, 16
4=64
here 48 is near to 54 and 48 goes 3 times
54 * 3= 162
right
means 163/3 gives 54
1st pattern is /3
step2: rela b/w 54,18
since we got /3 as pattern chech with /3 first
18 * 3 = 54
if here same pattern doesnt satisfy we need to go for increasing/ decresing pattern check
mostly by seeing series we can say whether pattern is in increasing/ decreasing order because if pattern is in decresing order chances of same pattern
mostly given inincreasing pattern only so check increasing pattern first, if it doesnt satisfy then go for decresing
means 54/3 = 18
here also pattern /3
step3: rela b/w 18,6
means 18/3 is 6
use same pattern, 6 * 3 = 18
here also pattern is /3
step4: calsulate this pattern with lat numb inorder to get next numb in series
6/3 = 2
next numb in series is 2
algorithm:
step1: check relation b/w 1st two numbers
and here you will get underlying pattern b/w 1st two numbers(and this pattern belong to fist numb)
step2: now chech pattern b/w 2nd and 3rd numb
here what trick you need to do is use the pattern you got in step 1 here
like check this 2 numbers with same pattern if it works it means whole series follows same pattern
if it doesnt work means the pattern is either in increasing / decresing order
chech one numb more than pattern we got if it satisfies then pattern is in increasing order, if it doesnt work
check one numb below, (if both above same and increasing dint work means it is definitely in decresing order) here you will get pattern in decresing order
we may sometimes have alternate patterns also apart from above 3 patterns it is like /2, /3, /2, /3 but this kind od pattern is not seen in above 4 cases and seen in combination series
consecutive series
c.n means numbers are in sequence order after one another without any numb skipping b/w them
ex: 1,2,3,4,5,6,7 (consecutive natural)
if you look at all the examples, we picked numbers in sequence without skipping any num in b/w or without considering alternate numbers
like for even consecutive series, we took all even numbers in sequence without skipping any numb/ or not considering alternate. similiarly we took for odd, multiples, decreasing
similarly like this we may also have consecutive squares, consecutive cubes, consecutive primes, consecutive non-primes
if consecutive is not mentined they could be irregularyly increasing/ decreasing
ex: square series: 4,16,36,64
if you look at above example the series is squares of numb not in an sequence
like 2^2, 4^2, 6^2, 8^2
although they can also be considered as consecutive even square series( but just for example consi as non consicutive series just for undersatnding purpose of non- consecutive series)
since here underlying pattern is in even consecutive we can say the series is also even consecutive
a proper example of non consecutive series
13,16,18,21,28
not in sequence, whether you take multiples/ squares/ or any underlying pattern
types of consecutive series
consecutive odd
3,5,7,9,11
consecutive multiples of 5
25,30,35,40,45
consecutive even
ex: 4,6,8,10,12
consecutive decreasing
8,7,6,5,4
questions
here he will give a series and asks us to find next numb in series
algorithm to find ans
check whether pattern is familiar or not
means check whether given pattern has natural numbers in sequence, squares, cubes, primes, non-primes, multiples os any table (whether in increasing or increasing order as per series)
if not familiar
calculate diff b/w easch two numb in series to get underlying pattern
here is the series is in increasing order(from left to right), then consider + to pattern it means you need to add this numb
if pattern is in decresing order(left to right), consider - to pattern, it means you need to subtract this numb
since we are talking about pattern there are 3 types of pattern
increasing order: 1,2,3,4,5,6
based on series we can give +/- to this pattern
decreasing order: 8,7,6,5,4,3
same pattern means 3,3,3,3,3
calculate last numb in series with the pattern of its before numb in series to get next numb in series
addition series
in addition series the series are always in increasing order
if a question falls in this addition series it means it is not familiar
because if it is familiar, it can be solved with squares, cubes, multiples or anything and dont in hold for difference, because in addition seres we calculate difference
question:
here he will give a series which is in normal increment(will be unfamiliar)
ex: 4,9,15,22,30,39,?
10th problem in exmaples
consider biggest numb and series and calculate diff b/w them, you will get one pattern which belong to first numb in series in b/w the numbers you calculated
39-30= 9
pattern is 5,6,7,8,9
repeat this pattern calculation for all numbers and at end you will be having pattern of whole series
if the pattern is same, add same pattern to last in series to get next numb
if the pattern is in increasing order, consider next big number of the pattern and add this next big num to last numb to get next numb in series
next big num of pattern is 10
now 10 + last digit to get next numb
10 + 39 =49
49 is ans
pattern
here pattern could be same, natural numb, squares, alternate numb, alternate primes, primes, it could be anything, but definitely will be in increasing order
subtraction series
subtraction series is in normal decreasing order
multiplication (direct multiplication)
if a series belong to multiplication series the chances of it may be
multi with subtraction series
multiplication with fraction series
multi with addition series