Question

What is the 10th term of the following geometric sequence?

7/9, -7/3, 7, -21,63

A. -5103
B. 5103
C. 15,309
D. -15,309

Answer 1

an find the common ratio by dividing the second term by the first term
(-7/3) / (7/9) = -7/3 * 9/7 = -21/7 reduces to -3 <== common ratio

an = a1 * r^(n - 1)
n = term to find = 10
a1 = first term = 7/9
r = common ratio = -3

now we sub
a10 = 7/9 * -3^(10 - 1)
a10 = 7/9 * -3^9
a10 = 7/9 * -19683
a10 = - 137781 / 9
a10 = - 15309 <==