What is the next number in the sequence: 2, 6, 22, 56, 114?

Question

A. 202
B. 228
C. 232
D. 245
E. 281

chetan2u · Answer

There are no set rules when it comes to sequence/patterns.

It could be as weird as each number being  n^3-n^2 , {0, 4, 18, 58,….} or as simple as difference between consecutive terms being 2 {1,3,5….}
So, some can give you an answer straight way and some would require hit and trial.

Back to the question

The common difference is not same, and they do not fall in pattern of squares cubes etc. Rather I tried with  2^2-2, 3^2-3 , but it ended there because next should have been  4^2-4  or 12.

So, it was 4th or 5th trial that I stumbled upon the correct (or should I say one of the correct ) pattern.

Took out the difference between each consecutive terms. 
 (6-2),(22-6),(56-22),(114-56)…… 
 4,16,34,58…… .  No pattern that can justify each number.

So, went with one more difference. 
 (16-4),(34-16),(58-34)…… 
 12,18,24……… . Ok, so I have a pattern here.  Each difference of difference increases by 6.

Next, should be 24+6 or 30 and D-58=30 or D=88, where D is the difference between 114 and next term. 
Thus, answer is 114+88 or 202.

A

Why the entire theory above and not the solution straight way? 
It is to tell you that the patterns do not have any straight answers. The higher ones may require some thinking, so don’t get worried if you don’t get the answer. 
You will not see such a question on GMAT. It will just help you in exercising your brain a bit.

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

https://www.youtube.com/watch?v=4sZjmquxnU4

Sequence: 2, 6, 22, 56, 114?

Lets try to figure out the pattern
First term = 2 = 1*2
Second Term = 6 = 2*3
Third term = 22  ≠ 3*4
 => Not following this pattern

Lets try subtracting the terms form each other
6 - 2 = 4
22 - 6 = 16
56 - 22 = 34
114 - 56 = 58

1. Pattern of differences 
4 =  4^1 
16 =  4^2  
34  ≠   4^3 
 => Not following this pattern

2. Lets subtract the terms again 
16 - 4 = 12
34 - 16 = 18
58 - 34 = 24

12, 18, 24 follow a pattern => previous term + 6
=> Next term will be 24 + 6 = 30

=> Corresponding number in step 2 above
 x - 58 = 30
=> x = 88

=> Corresponding number in step 1 above 
y - 114 = 88
y = 114 + 88 = 202

So,  Answer will be A 
Hope it helps!

Watch the following video to MASTER Sequences

https://www.youtube.com/watch?v=EfNT2JoE5CM

pappal · Answer

in such questions we observe the sequence patterns and proceed
1st term=1^3-(-1), 2nd term=2^3-2, 3rd term=3^3-5, 4th term=4^3-8, 5th term=5^3-11
means as n=1,2,3..... proceeds its cube is reduced by adding 3 to the first value starting from -1.
OR
Tn (general term)= n^3-  .
so next term =6^3- =216-14=202 
A

Adit_ · Answer

Any sequence to get a feel for it, you need to start with the pyramid wise top down approach.
Meaning:
Keep finding the difference down to the final one recursively till u hit on a pattern, This almost always works unless u add squares or cubes of numbers and so forth in which case its harder ofc.

In this case thought its just simply addition recursivly done.

1) First step of difference between numbers:
4,16,34,58

2) Now find the diff among the diff of the first step:
12,18,24

Now find the diff again of the diff in step two:
=6,6,6
Now you can see that we have hit on a uniform set of differences! Which is our pattern.

Now move upwards keeping the same 6 diff as constant and move to step 1.

Which means 24+6 = 30 as difference. Now move to step 1, 58 + 30 = 88
Our final answer = 114+88 = 202.

Answer:  Option A

What is the next number in the sequence: 2, 6, 22, 56, 114?

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GMAT Problem Solving (PS) Questions

What is the next number in the sequence: 2, 6, 22, 56, 114?

Prep Toolkit

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