Find the ninth term of the following geometric sequence

Question

a4=27 a7=64 i need a9

Answer 1

x_n = ar^(n-1)

a₄ = ar^(4-1) = 27 --> equation 1

a₇ = ar^(7-1) = 64 --> equation 2

2 equations in 2 unknowns

divide equation 1 by equation 2

r³ = 64 / 27 = (4/3)³

r = 4/3

substitute in equation 1

a = 27 / r³ = 3³ / (4/3)³ = 3⁶ / 4³

a₉ = ar⁸

a₉ = (3⁶ / 4³) x (4⁸ / 3⁸) = 4⁵ / 3² = 113.78