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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