MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 12

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The $n^{t h}$ term of a G.P. is $128$ and the sum of its $n$ terms is $225$ . If its common ratio is $2$ , then its first term is

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Important Questions on Geometric Progressions

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IMPORTANT

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 13

If second term of a G.P. is

2

and the sum of its infinite terms is

8

, then its first term is

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MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 14

If

a, b, c

are in G.P. and

x, y

are AM's between

a, b

and

b, c

respectively, then

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MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 15

If

A

be one A.M. and

p, q

be two G.M.'s between two numbers, then

2 A

is equal to

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MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 16

If

p, q

be two A.M.'s and

G

be one G.M. between two numbers, then

G^{2} =

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MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 17

If

x

is positive, the sum to infinity of the series

\frac{1}{1 + x} - \frac{1 - x}{(1 + x)^{2}} + \frac{(1 - x)^{2}}{(1 + x)^{3}} - \frac{(1 - x)^{3}}{(1 + x)^{4}} + \dots

is

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MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 18

If

(4^{3}) (4^{6}) (4^{9}) (4^{12}) \dots (4^{3 x}) = (0.0625)^{- 54},

the value of

x

is

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MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 19

Given that

x > 0,

the sum

\sum_{n = 1}^{\infty} {(\frac{x}{x + 1})}^{n - 1}

equals

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MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>MULTIPLE CHOICE QUESTIONS (MCQs)>Q 20

In a G.P. of even number of terms, the sum of all terms is five times the sum of the odd terms. The common ratio of the G.P. is