Directions (48-52): What will come in place of question mark (?) in the following questions.

4, 5, 13, 22, 86, ?

The correct answer is 111.

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

Given series: 4, 5, 13, 22, 86, ?

Let us look at the differences between successive numbers:

First difference: 5 - 4 = 1

Second difference: 13 - 5 = 8

Third difference: 22 - 13 = 9

Fourth difference: 86 - 22 = 64

Now, let us examine the pattern formed by these differences:

1 = 1³ (or 1²)

8 = 2³

9 = 3²

64 = 4³

We can observe an alternating pattern of squares and cubes of consecutive natural numbers:

Difference 1 = 1³ = 1

Difference 2 = 2³ = 8

Difference 3 = 3² = 9

Difference 4 = 4³ = 64

Following this alternating power pattern (cube, cube, square, cube, square... or alternating 5²):

The next difference should be 5² = 25.

Therefore, the missing term (?) can be calculated as:

86 + 25 = 111

Hence, the number that comes in place of the question mark is 111.