In the number series 2, 5, 13, 31, 69, the next term is _______. – UGC NET Question

Each new term is obtained by doubling the previous term and then adding consecutive odd numbers. From 2 to 5 we apply 2×2+1, from 5 to 13 we use 5×2+3, from 13 to 31 we use 13×2+5, and from 31 to 69 we use 31×2+7. The series of added odd numbers is 1, 3, 5, 7, so the next odd number must be 9. Therefore the next term is 69×2+9 = 147.

Option A:
Option A would correspond to 69×2+5, reusing an earlier odd adjustment instead of moving to 9. This would make the added sequence 1, 3, 5, 7, 5, which does not show a clear progression. As such, 143 does not respect the steadily increasing odd-number adjustment rule.

Option B:
Option B equals 141, which would arise from 69×2+3. That uses an even smaller odd addition than in the previous step, reversing the pattern 1, 3, 5, 7. Hence 141 cannot be justified by the observed rule.

Option C:
Option C uses 69×2+9, giving 147 and continuing the series of added odd numbers as 1, 3, 5, 7, 9. This maintains both the doubling structure and the simple progression among the adjustments. Therefore 147 is the correct next term.

Option D:
Option D, 151, would require adding 13 to 69×2, jumping from an added 7 directly to 13 and skipping 9 and 11. This breaks the neat sequence of consecutive odd numbers that defines the pattern. Thus 151 is not a valid extension.