Question

How do you find the 10th term in the geometric sequence 25, 5, 1, 0.2, ...?

Answer 1

a = 25

r = 5/25 = 1/5

10th term = a × r^9

$= 25 \times { (\frac{1}{5} )}^{9} \\ = {5}^{2} \times \frac{ {1}^{9} }{ {5}^{9} } \\ = \frac{ {5}^{2} }{ {5}^{9} } \\ = \frac{1}{ {5}^{7} } \\ = .0000128$