# geometric series

#### katiethegreat

Hey all

I was stuck with this question...
A geometric series has second term 375 and fifth term 81 .​
(a) (i) Show that the common ratio of the series is 0.6

I got as far as figuring out that ar= 375 and ar^4 = 81 ....but then i got confused.

Thanks xx

375 * .6^3 = 81

#### e^(i*pi)

MHF Hall of Honor
Hey all

I was stuck with this question...
A geometric series has second term 375 and fifth term 81 .​
(a) (i) Show that the common ratio of the series is 0.6

I got as far as figuring out that ar= 375 and ar^4 = 81 ....but then i got confused.

Thanks xx
Divide them

$$\displaystyle \frac{ar^4}{ar} = \frac{81}{375}$$

Working is in the spoiler, but remember you'll only be cheating yourself if you don't understand...

$$\displaystyle r = \sqrt[3]{\frac{81}{375}} = \sqrt[3]{\frac{27}{125}} = \sqrt[3]{\frac{3^3}{5^3}} = \frac{3}{5}$$