Hi All,
I need a hint for this one. I think I may be missing something here.
Find the first term and common ratio if,
$\displaystyle
33S_5 = S_{10}
$
$\displaystyle
S_{10} = S_9 + 5
$
Thanks for your help!
Hi All,
I need a hint for this one. I think I may be missing something here.
Find the first term and common ratio if,
$\displaystyle
33S_5 = S_{10}
$
$\displaystyle
S_{10} = S_9 + 5
$
Thanks for your help!
I suppose $\displaystyle S_5,S_9,S_{10}$ are, respectively, the sum of first 5,9 and 10 terms--right?
If this is the case and first term=$\displaystyle a$, ratio=$\displaystyle r$, then the sum of the GP series upto first $\displaystyle n$ terms will be
$\displaystyle S_n=a+ar+ar^2+ar^3+...+ar^{n-1}$
$\displaystyle =a[1+r+r^2+r^3+....+r^{n-1}]$
$\displaystyle =a\frac{r^n-1}{r-1}$
So your first equation reduces to $\displaystyle 33a\frac{r^5-1}{r-1}=a\frac{r^{10}-1}{r-1}$ and second equation reduces to $\displaystyle a\frac{r^{10}-1}{r-1}=a\frac{r^9-1}{r-1}+5$
Solve these two equations to get $\displaystyle a$ and $\displaystyle r$.