If in an infinite G.P., first term is equal to 10 times the sum o… - Vidyadip

MCQ

If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, the its common ratio is:

A
$\frac{1}{10}$
✓
$\frac{1}{11}$
C
$\frac{1}{9}$
D
$\frac{1}{20}$

✓

Answer

Correct option: B.

$\frac{1}{11}$

Let the first term of the G.P. be a.
Let its common ratio be r.
According to the question, we have:
First term = 10 [Sum of all successive terms]
$\text{a}=10\Big(\frac{\text{ar}}{1-\text{r}}\Big)$
$\Rightarrow\text{a}-\text{ar}=10\text{ar}$
$\Rightarrow11\text{ar}=\text{a}$
$\Rightarrow\text{r}=\frac{\text{a}}{11\text{a}}=\frac{1}{11}$

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