Identify the numbers that occur in the series 1, 1, 7, 17, 31, 49, ... Choose the correct answer from the options given below.

1.74

2.95

3.97

4.127

5.161

A1, 2 and 3 only

B3, 4 and 5 only ✓ Correct

C5, 2 and 1 only

D3, 4 and 2 only

Correct answer: (B) 3, 4 and 5 only

Explanation

The numbers 97, 127 and 161 occur in the series.

From the second term each follows 2n^2 - 1 for n = 1, 2, 3, ...

97 = 2 x 49 - 1 (n = 7) and 127 = 2 x 64 - 1 (n = 8).

161 = 2 x 81 - 1 (n = 9).

74 and 95 are not of the form 2n^2 - 1.

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