Question

500,491,478,449,384??​

Answer 1

Given series : 500,491,478,449,384...

Let us see the difference between the terms.

Difference between:

⟹ 500 and 491 = 9

⟹ 491 and 478 = 13

⟹ 478 and 449 = 29

⟹ 449 and 384 = 65

We get this : 9, 13, 29, 65....

We can not see equal difference between the terms, Try checking difference between the difference of each term.

Difference between:

⟹ 9 and 13 is 4

⟹ 13 and 29 is 16

⟹ 29 and 65 is 36

Now, we can see a pattern here, 4, 16 and 36 are square numbers.

⟹ 4 = 2²

⟹ 16 = 4²

⟹ 36 = 6²

They are squares of even numbers starting from 2.

So, the next would be : 8² = 64

The next number in the series will be :

Last number + 64

⟹ 65 + 64 = 129

The series of difference between the terms will be:

9, 13, 29, 65, 129

Now, we will subtract 129 from the last term of the original series, The next term will be :

⟹ 384 - 129

⟹ 255

255 is the next term.