First term of a G.P. is 7 , last term is 448 and sum of all terms is 889 , then common ratio is

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8. Sequences and Series

easy

The first term of a $G.P.$ is $7$, the last term is $448$ and sum of all terms is $889$, then the common ratio is

A

$5$

B

$4$

C

$3$

D

$2$

Solution

(d) $a = 7\,\,{\rm{and}}\,\,a{r^{n – 1}} = 448$

Now,${S_n} = \frac{{a({r^n} – 1)}}{{r – 1}} = 889$

$ \Rightarrow \frac{{(a{r^{n – 1}}.r – a)}}{{r – 1}} = 889$

==> $\frac{{448r – 7}}{{r – 1}} = 889$

==> $r = 2$.

Standard 11

Mathematics

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