Question
For a G.P.
If $a=2, r=3, S_n=242$, find $n$.
If $a=2, r=3, S_n=242$, find $n$.
✓
Answer
$a=2, r=3, S_n=242$
$S_n=a\left(\frac{r^2-1}{r-1}\right), \text { for } r>1$
$\therefore 242=2\left(\frac{3^n-1}{3-1}\right)$
$\therefore 242=3^n-1$
$\therefore 3^n=243$
$\therefore 3^n=3^5$
$\therefore \quad n=5$
$S_n=a\left(\frac{r^2-1}{r-1}\right), \text { for } r>1$
$\therefore 242=2\left(\frac{3^n-1}{3-1}\right)$
$\therefore 242=3^n-1$
$\therefore 3^n=243$
$\therefore 3^n=3^5$
$\therefore \quad n=5$
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