SOLUTION: A geometric series has 8 terms whose sum of the first three terms is 13/9 and the sum of the last three terms is 351. Find the first term and the common ratio of the series

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Question 1073866: A geometric series has 8 terms whose sum of the first three terms is 13/9 and the sum of the last three terms is 351. Find the first term and the common ratio of the series
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let us define
r= common ratio
x= the first term

The first three terms are:
x= the first term,
xr= the second term, and
xr%5E2= the third term.
Their sum is
x%2Bxr%2Bxr%5E2=x%281%2Br%2Br%5E2%29=13%2F9 .

The last three terms are:
xr%5E5= the sixth term,
xr%5E6= the seventh term, and
xr%5E7= the eight term.
Their sum is

r%5E5=351%289%2F13%29=351%2A9%2F13
r%5E5=%283%5E3%2A13%29%2A%283%5E2%29%2F13
r%5E5=3%5E5
highlight%28r=3%29
Substituting into
x%281%2Br%2Br%5E2%29=13%2F9 ,
x%281%2B3%2B3%5E2%29=13%2F9
x%281%2B3%2B9%29=13%2F9
13x=13%281%2F9%29
highlight%28x=1%2F9%29