Question

the first term of a geometric sequence is 45. write the next three terms if the sum of all of the terms of the sequence is 27.

Answer 1

45/(1 - r) = 27

5/(1 - r) = 3

3(1 - r) = 5

1 - r = 5/3

r = -2/3

First term is 45.

Second term is 45(-2/3) = -30.

Third term is -30(-2/3) = 20.

Fourth term is 20(-2/3) = -40/3 = -13 1/3.