Question

What is the 19th term of a geometric sequence where
a_1=14
and
a_9=358.80
? Round the common ratio and 19th term to the nearest hundredth.

Answer 1

well a term in a geometric series is

\[a_{n} = a_{1} \times r^{n - 1}\]

so you know the 9th term, use it to find the common ratio

\[358.8 = 14 \times r^{9 -1}\]

which becomes

\[r^8 = \frac{358.8}{14}\]

solve for r then you can use the formula above to find the 19th term

Answer 2

so then r is approximately 1.5?

Answer 3

thats correct

Answer 4

Thank you!