Question

Make a conjecture as to what number comes is next
-15,-10,-4, 3, 11, ______

Answer 1

Given:

The sequence is:

-15,-10,-4, 3, 11, ______

To find:

The next number.

Solution:

We have,

-15,-10,-4, 3, 11, ______

Here, the difference between two consecutive terms are:

`-10-(-15)=-10+15`

`-10-(-15)=5`

Similarly,

`-4-(-10)=6`

`3-(-4)=7`

`11-3=8`

It is clear that the difference difference between two consecutive terms is increasing by 1. So, the next difference must be (8+1)=9.

Let the next number be x. Then,

`x-11=9`

`x=9+11`

`x=20`

Therefore, the next number of the sequence is 20.