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 if the series is geometric you know

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

which can be used to find the common ratio.

\[358.8 = 14 \times r^8\]

so you need to solve for r, the common ratio

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

when you have r you can go and find the 19th term

\[a_{19} = a_{1} \times r^{19 -1}\]

hope this helps.