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.

Question

campbell_st · Answer

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.