In the number series 7, 9, 13, 15, 19, 21, the next term is _______. – UGC NET Question

The differences alternate between +2 and +4: 7→9 (+2), 9→13 (+4), 13→15 (+2), 15→19 (+4) and 19→21 (+2). Following this pattern, the next difference should be +4. Adding 4 to 21 gives 25. Therefore, 25 is the next term that maintains the alternating pattern.

Option A:
Option A is 23, which would add only 2 to 21 and repeat the smaller jump twice in a row. That contradicts the +2, +4 alternation visible in the earlier terms. Hence, 23 is not correct.

Option B:
Option B equals 25, obtained by 21 + 4 and continuing the established +2, +4, +2, +4, +2, +4 sequence of differences. This keeps the pattern consistent and regular. Thus, 25 is the appropriate next term.

Option C:
Option C is 27, representing a jump of 6 from 21, which has not appeared anywhere in the difference sequence. Introducing +6 here would break the simple alternation between +2 and +4. Therefore, 27 cannot be chosen.

Option D:
Option D is 29, which corresponds to an increase of 8 from 21 and departs even further from the observed pattern. As there is no justification for such a large jump, this option is not acceptable.