In the number series 1, 5, 13, 25, 41, 61, the next term is _______. – UGC NET Question

The first-level differences are 4, 8, 12, 16 and 20. These differences form an arithmetic progression with common difference 4. Consequently the next difference should be 24. Adding 24 to 61 gives 85 as the next term in the series. This choice keeps the second-level arithmetic pattern intact and yields a smooth numerical growth.

Option A:
Option A yields a difference of 20 from 61, merely repeating the last gap instead of extending it. The sequence of differences would become 4, 8, 12, 16, 20, 20, which breaks the constant increment of 4 between gaps. Hence 81 cannot be correct.

Option B:
Option B gives a difference of 22, so the jump from 20 to 22 is only 2. This violates the established rule that each new difference must be 4 more than the previous one. Therefore 83 does not align with the underlying structure.

Option C:
Option C would produce a difference of 28, so the step from 20 to 28 is 8, not 4. This makes the progression among the differences irregular and undermines the pattern. Thus 89 is not a suitable next term.

Option D:
Option D introduces a difference of 24, continuing the sequence of gaps 4, 8, 12, 16, 20, 24. This preserves the arithmetic progression at the second level and leads to 61+24 = 85. For this reason, 85 is the correct continuation.