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.