Question

What are the next two numbers in the pattern of numbers;
45, 15, 44, 17, 40, 20, 31, 25, …

Answer 1

The next two numbers in the pattern of numbers:-

45, 15, 44, 17, 40, 20, 31, 25, 15, 32

Step-by-step explanation:

In the given pattern, there are two sets of numbers. Every alternate number follows a similar pattern.

Taking the first set of alternate numbers -

45, 44, 40, 31 __?

The difference between the above numbers is -1, -4, -9

If we observed, this becomes a series of perfect squares.

$- 1 = {1}^{2}$

$- 4 = {2}^{2}$

$- 9 = {3}^{2}$

Hence, the next difference should be -16. So, the next number in the first series is 31 - 16 = 15.

45, 44, 40, 31, 15.

_______________________________

Taking the second set of alternate numbers

15, 17, 20,25, __ ?

The difference between the above numbers is 2, 3, 5,

If we observed, this becomes a succession of prime numbers. So, the next prime number is 7.

Hence, the next number in this series should be 32.

15, 17, 20, 25, 32.

Hence, the pattern is 45, 15, 44, 17, 40, 20, 31, 25, 15, 32.