For a given geometric sequence, the 8th term, a8, is equal to 13/16, and the 13th term, a13, is equal to −26 . Find the value of the 15th term, a15. If applicable, write your answer as a fraction.

Answer 1

A8 = 13/16

A13 = -26

ar^8 = 13/16

ar^13 = -26

r<0 A15<0 the signs alternate

ignoring the signs, r^13 = r^8 x r^5 = 26 = 13/16 x r^5

r^5 = 26 x 16/13 = 32

r = 5th root of 32 = 2

the common ratio = -2

A15 = A13 x r^2 = -26 x 4 = -104

A8 = 13/16

A9= 13/16 x -2= - 13/8

A10 = -13/8 x -2 = 13/4

A11 = 13/4 x -2 = -13/2

A12 = -13/2 x -2 = 13

A13 = 13 x -2 = -26

A14 = -26 x -2 = 52

A15 = 52x -2 = -104