In the number series 11, 30, 65, 120, 199, the next term is _______. – UGC NET Question

The first-level differences are 19, 35, 55 and 79. The second-level differences are 16, 20 and 24, which themselves increase by 4. Continuing this pattern, the next second-level difference should be 28, so the next first-level difference becomes 79+28 = 107. Adding 107 to 199 yields 306, which keeps both levels of the pattern coherent.

Option A:
Option A gives 300, corresponding to a difference of 101 from 199. This would make the second-level differences 16, 20, 24 and 22, breaking the rule that these grow by 4 each time. Thus 300 is not consistent with the established structure.

Option B:
Option B gives 306, implying a difference of 107 from 199. The differences become 19, 35, 55, 79, 107 and the second-level differences are 16, 20, 24, 28. This preserves the steady +4 growth at the second level, so 306 is the correct continuation.

Option C:
Option C gives 310, which corresponds to a difference of 111 from 199. That would produce a second-level jump from 79 to 111 equal to 32, not 28, making the pattern irregular. Hence 310 cannot be accepted.

Option D:
Option D gives 314, yielding a difference of 115 from 199. The last second-level step would become 36, which further disrupts the neat arithmetic progression. Therefore 314 is not a valid next term.