SOLUTION: A geometric sequence has four positive terms a1,a2,a3,a4. If a3/a1=9 and a1+a2=4/3, then what is a3?

Algebra ->  Sequences-and-series -> SOLUTION: A geometric sequence has four positive terms a1,a2,a3,a4. If a3/a1=9 and a1+a2=4/3, then what is a3?      Log On


   

Question 1168533: A geometric sequence has four positive terms a1,a2,a3,a4. If a3/a1=9 and a1+a2=4/3, then what is a3?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
If common ratio is r then a%5B3%5D%2Fa%5B1%5D=r%5E2=9 and therefore highlight_green%28r=3%29.

Given a%5B1%5D%2Ba%5B2%5D=4%2F3
and from use of the ratio found,
a%5B1%5D%2Ba%5B1%5D%2A3=4%2F3
.
.
highlight_green%28a%5B1%5D=1%2F3%29

From that, term at index 3 is %281%2F3%29%2A3%5E2=highlight%283%29.