MCQ
The first term of a $G.P.$ whose second term is $2$ and sum to infinity is $8$, will be
- A$6$
- B$3$
- ✓$4$
- D$1$
✓
Answer
Correct option: C.
$4$
c
(c) We have $ar = 2$ and ${S_\infty } = 8 = \frac{a}{{1 - r}}$
(c) We have $ar = 2$ and ${S_\infty } = 8 = \frac{a}{{1 - r}}$
$ \Rightarrow $ $8 = \frac{2}{{r(1 - r)}}\left( {\;a = \frac{2}{r}} \right)$
$ \Rightarrow $ $4r(1 - r) = 1 $
$\Rightarrow 4r - 4{r^2} - 1 = 0$
$ \Rightarrow $ $4{r^2} - 4r + 1 = 0$
$\Rightarrow \left( {r - \frac{1}{2}} \right)(4r - 2) = 0$
$\Rightarrow r = \frac{1}{2}$
So first term $a = 4$.
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