What will come in the place of question (?) mark in following number series:
1834, 1618, 1593, 1529, ?, 1512

The correct option is 1520.

To find the missing number in the series, let us analyze the differences between consecutive terms:

1^st difference: 1834 - 1618 = 216

2^nd difference: 1618 - 1593 = 25

3^rd difference: 1593 - 1529 = 64

Notice that these differences are exact powers of consecutive integers:

216 = 6³

25 = 5²

64 = 4³

Following this pattern, the differences alternate between cubes and squares of decreasing integers (6³, 5², 4³, 3², 2³, ...):

4^th difference should be 3² = 9.

Therefore, the missing number (?) is calculated as:

1529 - 9 = 1520

We can verify the last term using the next difference (2³ = 8):

1520 - 8 = 1512

This matches the given final term in the series. Thus, the missing number is 1520.