(A) The given $G.P.$ is $0.15, 0.015, 0.0015, \dots$Here,the first term $a = 0.15$ and the common ratio $r = \frac{0.015}{0.15} = 0.1$.The sum of $n$

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(A) The given $G.P.$ is $0.15, 0.015, 0.0015, \dots$Here,the first term $a = 0.15$ and the common ratio $r = \frac{0.015}{0.15} = 0.1$.The sum of $n$ terms of a $G.P.$ is given by $S_{n} = \frac{a(1-r^{n})}{1-r}$.For $n = 20$,we have $S_{20} = \frac{0.15[1-(0.1)^{20}]}{1-0.1}$.$S_{20} = \frac{0.15}{0.9}[1-(0.1)^{20}]$.$S_{20} = \frac{15}{90}[1-(0.1)^{20}]$.$S_{20} = \frac{1}{6}[1-(0.1)^{20}]$.

Class 11 Mathematics Sequences and Series Geometric progression

Easy

Find the sum up to $20$ terms in the geometric progression $0.15, 0.015, 0.0015, \dots$

A
$\frac{1}{6}[1-(0.1)^{20}]$
B
$\frac{1}{9}[1-(0.1)^{20}]$
C
$\frac{1}{3}[1-(0.1)^{20}]$
D
$\frac{1}{12}[1-(0.1)^{20}]$

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Geometric progression

If the first term of a Geometric Progression $(GP)$ is $1$ and the sum of its third and fifth terms is $90$,find the common ratio.

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If $a, b, c, d$ and $p$ are distinct real numbers such that $(a^2 + b^2 + c^2)p^2 - 2p(ab + bc + cd) + (b^2 + c^2 + d^2) \leq 0$,then:

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If the ratio of the sum of the first three terms and the sum of the first six terms of a $G.P.$ is $125 : 152$,then the common ratio $r$ is:

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If $G$ is the geometric mean of $x$ and $y$,then $\frac{1}{G^2 - x^2} + \frac{1}{G^2 - y^2} = $

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The interior angles of an $n$-sided convex polygon are in $G.P.$ The smallest angle is $1^\circ$ and the common ratio is $2$. Then the number of possible values of $n$ is:

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Find the sum up to $20$ terms in the geometric progression $0.15, 0.015, 0.0015, \dots$

Similar Questions

If the first term of a Geometric Progression $(GP)$ is $1$ and the sum of its third and fifth terms is $90$,find the common ratio.

If $a, b, c, d$ and $p$ are distinct real numbers such that $(a^2 + b^2 + c^2)p^2 - 2p(ab + bc + cd) + (b^2 + c^2 + d^2) \leq 0$,then:

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