In the number series 4, 9, 19, 34, 54, 79, the next term is _______. – UGC NET Question

The differences between the terms are 5, 10, 15, 20 and 25. These differences form a sequence of multiples of 5, increasing by 5 each time. The next difference should therefore be 30. Adding 30 to the last term 79 gives 79 + 30 = 109, which respects the established pattern in the differences.

Option A:
Option A gives 104, which is 25 more than 79 and simply repeats the last difference instead of increasing it. This breaks the rule that the increments themselves must grow by 5. Thus, 104 is not consistent with the pattern.

Option B:
Option B offers 107, corresponding to a difference of 28 from 79, which is not a multiple of 5 and does not fit the multiples-of-five structure. Therefore, 107 cannot be accepted as correct.

Option C:
Option C yields 109, which is 30 greater than 79 and continues the sequence of differences 5, 10, 15, 20, 25, 30. This makes the series mathematically coherent. Hence, 109 is the correct next term.

Option D:
Option D suggests 111, giving a difference of 32 from 79, which does not align with the multiples-of-5 pattern. Including 111 would disrupt the clear second-level arithmetic progression. Therefore, 111 is not appropriate.