Geometric Sequence

Question

For a given geometric sequence, the 8th term, a₈, is equal to 29/25, and the 11th term, a₁₁, is equal to -145. Find the value of the 13th term, a₁₃. If applicable, please write the answer as a fraction.

Answer 1

a₁₁ = a₈r²

-145 = (29 / 25)r²

-125 = r²

-5i√5 = r

a₁₃ = a₁₁r²

a₁₃ = -145(-125)

a₁₃ = 18 ,125

Answer 2

An = C R^n-1

29/25 = C R^7

-145 = C r^10

multiplies to first equation by 5---> 145/25 = 5C R^7

divides the 2nd equation by -25 ---> 145.25 = C/-25 R^10

5C R^7 = C/-25 R^10

5 = (-1/25) R^3

-125 = R^3

R = -5

then -145 = C (-5)^10

C = -145/(-5)^10 = -145/9765625

= -29/1953125

A(n) = (-5)^(n-1) * (-29)/(1953125)