Question

In a G.P. the first term is $7$, the last term $448$, and the sum $889$; find the common ratio.

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

Answer: (A)

$2$

$a,ar,a{r}^2$ , $a{r}^3$ , ........................$a{r}^n$ be the G. P
Let common ratio $=r$
and let $a_n$ be the nth term of G.P
Given that the first term$,a=7,$

$a_n=a{r}^{n-1}=448$ and

$S_n=\frac{a(r^n-1)}{r-1}=889$

$\Rightarrow S_n=\frac{a{r}^{n-1}r-a}{r-1}=889$

$\Rightarrow 448r-7=889r-889$

$\Rightarrow 882=441r$

$\Rightarrow r=2$