Chapter 11, Problem 15CUR

To determine

To Find:

The next number in the sequence.

Answer to Problem 15CUR

-45

Explanation of Solution

Given:

10, 9, 5, -4, -20.

Checking the difference in each consecutive term:

Difference between first and second term = 9-10=-1

Difference between second and third term = 5-9=-4

Difference between third and fourth term = -4-5=-9

Difference between first and second term = -20-(-4) = -16

It can be seen that the difference between consecutive terms (-1, -4, -9, -16) is in the form of squares of consecutive numbers i.e. 1, 2, 3, 4.

So, next difference should be square of 5 i.e. difference should be -25.

Therefore, next term = -20-25 = -45