Geometric Progression - ICSE STD 10 Mathematics Questions

Q 1[3 marks sum]3 Marks

The first term of a GP is 27 and its 8th term is $\frac{1}{81}$. Find the sum of its first 10 terms.

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Q 2[3 marks sum]3 Marks

The sum of $n$ terms of a progression is $3^n-1$. Show that it is a GP. Find its common ratio.

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Q 3[3 marks sum]3 Marks

How many terms of the GP $1,4,16,64, \ldots$ will make their sum 5461 ?

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Q 4[3 marks sum]3 Marks

Determine the number of terms $n$ in the GP $T _1, T_2 \ldots \ldots T_n$, if $T _1=3, T_n=96$ and $S _n=189$.

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Q 5[3 marks sum]3 Marks

Find the sum : $243+324+432+\ldots$ up to $n$ terms.

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Q 6[4 marks sum]4 Marks

Find the sum of the following to $n$ terms $7+77+777+\ldots$ .

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Q 7[4 marks sum]4 Marks

Find the sum to $n$ terms of the series whose $n$th term is $2^n+3 n$.

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Q 8[4 marks sum]4 Marks

Find the least value of $n$ for which the sum $1+3+3^2+\ldots$ to $n$ terms is greater than $7000$.

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Q 9[4 marks sum]4 Marks

The sum of three numbers in GP is $38$ and their product is $1728$. Find the numbers.

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Q 10[4 marks sum]4 Marks

The sum of three numbers which are consecutive terms of an AP is 21 . If the second number is reduced by 1 , and the third is increased by 1 , we obtain three consecutive terms of a GP. Find the numbers.

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Q 11MCQ1 Mark

$\sum_{k=1}^{11}\left(2+3^k\right)=$

A
$\frac{41+3^{10}}{2}$
B
$\frac{41+3^{12}}{2}$
C
$41+3^{12}$
D
$\frac{44+3^{12}}{2}$

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Q 12MCQ1 Mark

Given a G.P. with $a=729$ and $7$th term as $64$ , then $S _7=$

A
2059
B
462
C
-2061
D
2060

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Q 13MCQ1 Mark

________terms of the G.P. $3, \frac{3}{2}, \frac{3}{4}, \ldots$ are needed to give the sum $\frac{3069}{512}$.

A
9
B
10
C
11
D
12

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Q 14MCQ1 Mark

If the sum of the G.P. $1,4,16 \ldots$ is $341$ , then the number of terms in the G.P. is :

A
8
B
6
C
5
D
10

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Q 15MCQ1 Mark

The sum of first 6 terms of the G.P. $1,-\frac{2}{3},-\frac{4}{9}, \ldots$. is :

A
$\frac{-133}{243}$
B
$\frac{133}{243}$
C
$\frac{793}{1215}$
D
$\frac{667}{1215}$

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Q 16Assertion (A) & Reason (B) MCQ1 Mark

Assertion (A) : The sum of first 9 terms of the GP 3,6,12, $\ldots$ is 1533.
Reason (R) : The sum of first $n$ terms of a GP is given by $S _n=\frac{a\left(r^n-1\right)}{r-1}$.

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Q 17Assertion (A) & Reason (B) MCQ1 Mark

Assertion (A) : If the 5th term of a GP is 2 , then the product of its first nine terms is 510 .
Reason (R) : The $n$th term of a GP is given by $T _n=a r^{n+1}$.

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Q 18Assertion (A) & Reason (B) MCQ1 Mark

Assertion (A) : The sequence $2,6,18, \ldots$ is a GP.
Reason (R) : If the numbers $a_1, a_2, a_3, \ldots .$. are in GP, then ccommon ratio of the GP is $\frac{a_1}{a_2}$ or $\frac{a_2}{a_3}$

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Geometric Progression question types

Geometric Progression questions

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Geometric Progression Mathematics - Geometric Progression

Geometric Progression question types

Geometric Progression questions

Generate a Geometric Progression paper free