the sum of the first three terms of geometric proggression is 27 and first term is 36 determine the common ratio and the value of the fourth term

Answer 1

a + ar + ar^2 = 27
but a = 36
36 + 36r + 36r^2 - 27 = 0
divide each term by 9 and simplify
4r^2 + 4r + 1 = 0
(2r + 1)^2 = 0
2r + 1 = 0
r = -1/2

so fourth term = 36(1/2)^3 = 9/2