MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.4>Q 12

MEDIUM

11th CBSE

IMPORTANT

Earn 100

Show that in an infinite $G . P .$ with common ratio $r (| r | < 1)$ , each term bears a constant ratio to the sum of all terms that follow it.

Important Questions on Geometric Progressions

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.4>Q 13

If

S

denotes the sum of an infinite

G . P .

and

S_{1}

denotes the sum of the squares of its terms, then prove that the first term and common ratio are respectively

\frac{2 S S_{1}}{S^{2} + S_{1}}

and

\frac{S^{2} - S_{1}}{S^{2} + S_{1}}

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.5>Q 1

If

a, b, c

are in

G . P .

, prove that

\log a, \log b, \log c

are in

A . P

.

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.5>Q 2

If

a, b, c

are in

G . P .

, prove that

\frac{1}{\log_{a} m}, \frac{1}{\log_{b} m}, \frac{1}{\log_{c} m}

are in

A . P

.

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.5>Q 3

Find

k

such that

k + 9, k - 6

and

4

form three consecutive terms of a

G . P

.

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.5>Q 4

Three numbers are in

A . P .

and their sum is

15

. If

1, 3, 9

be added to them respectively, they form a

G . P

. Find the numbers.

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.5>Q 5

The sum of three numbers which are consecutive terms of an A.P. is

21

. If the second number is reduced by

1

and the third is increased by

1

, we obtain three consecutive terms of a G.P. Find the numbers.

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.5>Q 6

The sum of three numbers

a, b, c

in

A . P .

is

18

. If

a

and

b

are each increased by

4

and

c

is increased by

36

, the new numbers form a

G . P

. Find

a, b, c

.

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 20 - Geometric Progressions>EXERCISE 20.5>Q 7

The sum of three numbers in

G . P .

is

56

. If we subtract

1, 7, 21

from these numbers in that order, we obtain an

A . P

. Find the numbers.