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

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.

campbell_st · Answer

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

deadshot · Answer

so then r is approximately 1.5?

campbell_st · Answer

thats correct

deadshot · Answer

Thank you!