What is the next number in the sequence: 2, 6… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Sequences

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

Answer Choices

Correct answer marked below

202

Correct

228

232

245

281

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Explanation

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Official Explanation

Official

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

.…

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What this question tests

What it tests

Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.

Common trap

Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.