NIMCET 2012 — Reasoning PYQ

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Question

NIMCET 2012 — Reasoning PYQ

NIMCET | Reasoning | 2012

Find the odd number in the following series: $2, 9, 28, 65, 126, 216, 344, \dots$

Choose the correct answer:

Explanation

The pattern of the series is based on the cubes of natural numbers incremented by $1$ . The general formula for the $n^{th}$ term is:

T_n = n^3 + 1

Let's check each term:

First term: $1^3 + 1 = 1 + 1 = 2$
Second term: $2^3 + 1 = 8 + 1 = 9$
Third term: $3^3 + 1 = 27 + 1 = 28$
Fourth term: $4^3 + 1 = 64 + 1 = 65$
Fifth term: $5^3 + 1 = 125 + 1 = 126$
Sixth term: $6^3 + 1 = 216 + 1 = \mathbf{217}$
Seventh term: $7^3 + 1 = 343 + 1 = 344$

As we can see, the sixth term should be 217, but the number given in the series is 216.

Therefore, the odd number in the series is 216.

Correct Option: (d)