In the number series 2, 5, 9, 14, 20, the next term is _______. – UGC NET Question

The differences between terms are 3, 4, 5 and 6, which increase by 1 each time. So the next difference should be 7. Adding 7 to the last term 20 gives 27. Therefore, 27 continues the pattern of increasing differences correctly.

Option A:
Option A uses the new difference of 7, producing 20 + 7 = 27 and extending the sequence of differences to 3, 4, 5, 6, 7. This maintains a clear second-level arithmetic pattern. Hence, 27 is the correct next term.

Option B:
Option B is 26, which would give a difference of 6 from 20, repeating the previous step instead of increasing it. That breaks the systematic growth of the differences. Thus, 26 is not consistent with the rule.

Option C:
Option C is 28, implying a difference of 8 from 20, which jumps beyond the next expected difference of 7. This oversteps the gradual increase and makes the pattern irregular. Therefore, 28 cannot be correct.

Option D:
Option D is 30, which would require a difference of 10, a much larger jump than the expected 7. Such a sudden change has no support from earlier terms and spoils the structure. So, 30 is not suitable.