### Question

A. 71

B. 56

C. 65

D. 61

**Answer:** D

**Solution:**

These are given terms of series.

57, 56, 55, 51, 43, 34, ?

Differences of two consecutive terms can be calculated like this

57 – 56 = 1

56 – 55 = 1

55 – 51 = 4

51 – 43 = 8

43 – 34 = 9

34 – ? =

Now study the differences

1, 1, 4 , 8 , 9 , ….

This can be written as

1², 1³, 2², 2³, 3²,…..

In this pattern next difference would be 3³ and 4²

So next number would be 34 + 3³ = 34 + 27 = 61

And similarly next number would be 61 + 4² = 61 + 16 = 77

So answer = **61**