+47 120-80+160/3-320/9+....
Express your answer as a simplified fraction.
We are not here to do all your homework.
Multiple questions have been deleted.
Melody.
The common ratio r is \(-\frac{2}{3}\) How is it found? ----> \(\frac{a_2}{a_1}\) Since it is a geometric series.
This series is a finite (I.e. you just want the sum of the first 8 terms)
There is a formula for it which is:
\(S_n=\frac{a_1(1-r^n)}{1-r}\) , of course "r" can't be equal to 1
The first term we have is 120, common ratio is \(-\frac{2}{3}\) (r) and we want the sum of the first 8 terms so just substituting them will give you the answer.
\(\frac{120*(1-(-2/3)^8}{1-(-2/3)}\) Just simplify it.
