Question

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

Answer 1

Next two numbers are 15 and 32 respectively.

Explanation:

The given pattern is

45, 15, 44, 17, 40, 20, 31, 25, …

Here, we have two patterns.

Odd places : 45, 44, 40, 31,...

Even places : 15, 17, 20, 25,...

In series of odd places, we need to subtract square of integers.

`45-(1)^2=45-1=44`

`44-(2)^2=44-4=40`

`40-(3)^2=40-9=31`

So, 9th term of given pattern is

`31-(4)^2=31-16=15`

In series of even places, we need to add prime numbers.

`15-2=17`

`17+3=20`

`20+5=25`

So, 10th term of given pattern is

`25+7=32`

Therefore, the next two numbers in the pattern of numbers are 15 and 32 respectively.