In the number series 2, 5, 10, 17, 26, the next term is _______. – UGC NET Question

The differences in the series are 3, 5, 7 and 9, which form an increasing sequence of odd numbers. To continue this pattern, the next difference should be 11. Adding 11 to the last term 26 gives 26 + 11 = 37. This maintains the smooth growth of the differences and fits well with the structure of the given series. Therefore, 37 is the only option that preserves the observed pattern.

Option A:
Option A provides 37, which is obtained by adding the next odd difference 11 to 26. The difference sequence 3, 5, 7, 9, 11 remains perfectly consistent and shows a clear second level arithmetic pattern. This makes 37 the logically correct continuation of the number series.

Option B:
Option B gives 35, which corresponds to adding 9 to 26 and simply repeating the last difference instead of increasing it. This breaks the rule that differences themselves should grow by 2 each time. Hence, 35 does not correctly follow the pattern governing the series.

Option C:
Option C gives 38, which would require a difference of 12 from 26, overshooting the next expected odd difference of 11. This disrupts the systematic progression of differences and introduces an unjustified jump. Therefore, 38 is not a valid extension of the series.

Option D:
Option D suggests 40, which would create a difference of 14 from 26 and move even further away from the orderly sequence of odd differences. Such a large change is inconsistent with the established pattern of gradually increasing differences. Thus, 40 cannot be accepted as the next term.