Question

Complete the series 7,16,28,40,54,?

Answer 1

7, 16, 28, 40, 54,_____

When we examine this pattern we realize that it is an increasing pattern.

We need to find the pattern for the increase.

Lets take the prime numbers from 7 given that it is the smallest prime number in the series.

We have :

7, 11, 13, 17, 19, 23, 29,....

Lets subtract the prime numbers from the numbers as from 16 in that order from 11.

We have:

5, 15, 23, 35,

The difference is :

10, 8, 12..

The difference for this is :

-2, 4,..?

Using the concept of prime numbers, the next prime number after 2 is 3.

The next number is - 3. After this the next number is the square of -3.

This we observe from :

-2 and the next number is (-2)² which is 4.

Applying this in the patterns we get :

12 + - 3 = 9

35 + 9 = 44

44 + 23 = 67

The next number is thus 67.