A geometric series begins 10,5, 5/2, 5/4, 5/8, ... Find the common ratio r for this series and then the formula for the nth term of series, an. What is a10?

Question

A geometric series begins 10,5, 5/2, 5/4, 5/8, ... Find the common ratio r for this series and then the formula for the n^th term of series, a_n. What is a₁₀?

Answer 1

common ratio = r = 1/2

a1 = 10

an = a1(r^(n-1)

a10 = 10(.5^9) = 10(.0001953)

= .001953 = the 10th term

1953 is when IKE became president, when the movie Inherit the Wind premiered,

as the Korean War waged, inspiring the MASH TV series