Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.7>Q 3

EASY

11th ICSE

IMPORTANT

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A geometric progression consists of $n$ terms, where $n$ is odd. If the middle term of the $G . P .$ is $m$ , then what is the product of these $n$ terms.

Important Questions on Sequences and Series

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.7>Q 4

If the fourth term of a

G . P .

is

8

and fifth term is

16

, then what is the product of first

8

terms?

EASY

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IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.7>Q 5

If

G_{1}

and

G_{2}

are two

G . M .' s

between two positive numbers

a

and

b

, then show that

G_{1} G_{2} = a b

.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.7>Q 6

If

A_{1}, A_{2}

are two

A . M' s

and

G_{1}, G_{2}

are two

G . M' s

between two positive numbers

a

and

b

, then find the value of

\frac{A_{1} + A_{2}}{G_{1} G_{2}}

.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.7>Q 7

Insert

5

geometric means between

576

and

9

. Show that their product is equal to the fifth power of the single

G . M .

between the given numbers.

EASY

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IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.7>Q 8

The arithmetic mean between two numbers is

34

and

G . M .

is

16

. Find the numbers.

EASY

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IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.7>Q 9

The

A . M .

of two numbers

a

and

b

exceeds their G.M. by

2

. The ratio of two numbers is

4

. Find the numbers.

EASY

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IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.7>Q 10

Find two positive numbers whose difference is

12

and whose

A . M .

exceeds

G . M .

by

2

.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.7>Q 11

The arithmetic mean between two distinct positive numbers is twice the geometric mean between them. Find the ratio of greater to smaller.