In the number series 2, 3, 7, 16, 32, 57, the next term is _______. – UGC NET Question

The differences between consecutive terms are 1, 4, 9, 16 and 25. These differences are consecutive perfect squares: 1², 2², 3², 4² and 5². The next difference should therefore be 6² = 36. Adding 36 to the last term 57 gives 57 + 36 = 93, which continues the square-based pattern in the differences.

Option A:
Option A gives 88, corresponding to a difference of 31 from 57, which does not equal the next square 36. This contradicts the square structure underlying the series. Hence, 88 is not consistent with the pattern.

Option B:
Option B offers 90, whose difference from 57 is 33, again not matching 36 and making the pattern imprecise. Therefore, 90 cannot be accepted as correct.

Option C:
Option C suggests 92, which yields a difference of 35 from 57, only near but not equal to 36. This minor mismatch still breaks the strict square-difference rule. Thus, 92 is not appropriate.

Option D:
Option D yields 93, which is 36 more than 57 and extends the difference sequence 1, 4, 9, 16, 25, 36 in a perfectly regular way. This preserves the higher-level pattern. Therefore, 93 is the correct next term.