In the number series 5, 12, 23, 38, 57, the next term is _______. – UGC NET Question

The differences between the terms are 7, 11, 15 and 19. These differences increase by 4 each time, forming an arithmetic sequence at the second level. The next difference should therefore be 23. Adding 23 to the last term 57 gives 57 + 23 = 80, which extends the pattern smoothly.

Option A:
Option A gives 76, corresponding to a difference of 19, which merely repeats the last increment and does not allow the difference to grow to 23. This disrupts the pattern. Therefore, 76 is not correct.

Option B:
Option B offers 78, whose difference from 57 is 21, still short of the expected 23. This does not match the consistent addition of 4 at the level of differences. Hence, 78 cannot be accepted.

Option C:
Option C yields 80, which is 23 more than 57 and completes the difference sequence 7, 11, 15, 19, 23. This honours the second-level arithmetic progression. Thus, 80 is the correct next term in the series.

Option D:
Option D suggests 82, giving a difference of 25 from 57, which overshoots the expected value and makes the pattern uneven. Therefore, 82 is not appropriate.