geometric series

Jan 2010
12
0
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
 

e^(i*pi)

MHF Hall of Honor
Feb 2009
3,053
1,333
West Midlands, England
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...

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