Senior Secondary School Mathematics FOR CLASS 11>Chapter 11 - Arithmetic Progression>EXERCISE 11D>Q 4

MEDIUM

11th CBSE

IMPORTANT

Earn 100

Insert six arithmetic means between $11$ and $- 10$ .

Important Questions on Arithmetic Progression

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11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 11 - Arithmetic Progression>EXERCISE 11D>Q 5

There is

n

arithmetic means between

9

and

27

If the ratio of the last mean to the first mean is

2 : 1,

find the value of

n

.

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11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 11 - Arithmetic Progression>EXERCISE 11D>Q 6

Insert arithmetic means between

16

and

65

such that the

5^{th}

AM

is

51

. Find the number of arithmetic means.

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11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 11 - Arithmetic Progression>EXERCISE 11D>Q 7

Insert five numbers between

11

and

29

such that the resulting sequence is an

AP

.

HARD

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 11 - Arithmetic Progression>EXERCISE 11D>Q 8

Prove that the ratio of sum of

m

arithmetic means between the two numbers to the sum of

n

arithmetic means between them is

m : n .

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 11 - Arithmetic Progression>EXERCISE 11E>Q 1

If $a, b, c$ are in $A P,$ prove that

$(a - c)^{2} = 4 (a - b) (b - c)$

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 11 - Arithmetic Progression>EXERCISE 11E>Q 1

If $a, b, c$ are in $A P,$ prove that

$a^{2} + c^{2} + 4 a c = 2 (a b + b c + c a)$

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 11 - Arithmetic Progression>EXERCISE 11E>Q 1

If $a, b, c$ are in $A P,$ prove that

$a^{3} + c^{3} + 6 a b c = 8 b^{3}$

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 11 - Arithmetic Progression>EXERCISE 11E>Q 2

If $a, b, c$ are in $A P,$ show that

$(a + 2 b - c) (2 b + c - a) (c + a - b) = 4 a b c$