In the number series 9, 19, 33, 51, 73, the next term is _______. – UGC NET Question

The nth term of this series can be expressed as (a_n = 2n^2 + 1) for n starting from 2. For n = 2, 3, 4, 5 and 6, the values are 2·4+1 = 9, 2·9+1 = 19, 2·16+1 = 33, 2·25+1 = 51 and 2·36+1 = 73, which exactly match the given sequence. For n = 7, the expression yields 2·49+1 = 99. Hence 99 is the correct continuation of the series.

Option A:
Option A, 95, does not equal 2n²+1 for any integer n that naturally follows 2 to 6 here. Using 95 would force a change in the generating rule and so is inconsistent with the polynomial pattern.

Option B:
Option B, 97, also fails to satisfy the formula 2n²+1 for the next integer n. It appears close numerically but does not arise from the same expression, so it breaks the functional relationship.

Option C:
Option C, 98, lies between 97 and 99 but again does not equal 2·49+1. Adopting 98 would mean abandoning the clear square-based rule that explains all earlier terms.

Option D:
Option D, 99, matches precisely the value predicted by the formula for n = 7. Since the same expression generates each term, 99 preserves the structure and therefore is the correct next term.