# NCERT Solutions for Class 11-science Maths Chapter 9 - Sequences and Series

Page / Exercise

Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14

Solution 1
Solution 2
Solution 3
Solution 4
Solution 5

Solution 6
Solution 7
Solution 8
Solution 9
Solution 10

Solution 11

Solution 12
Solution 13

Solution 14
Solution 15
Solution 16

Solution 17
Solution 18

## Chapter 9 - Sequences and Series Exercise Ex. 9.3

Solution 1
Solution 2
Solution 3
Solution 4
Solution 5

Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15
Solution 16

Solution 17
Solution 18
Solution 19
Solution 20
Solution 21

Solution 22
Solution 23
Solution 24
Solution 25

a, b, c, d are in G.P.

Therefore,

b2 = ac      .....(2)

c2 = bd      .....(3)

It has to be proved that,

(a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2

R.H.S.

= (ab + bc + cd)2

= (ab + ad + cd)2  [Using (1)]

= [ab + d (a + c)]2

= a2b2 + 2abd (a + c) + d2(a + c)2

= a2b2 + 2a2bd + 2abcd + d2(a2 + 2ac + c2)

= a2b2 + 2a2c2 + 2b2c2 + d2a2 + 2d2b2 + d2c2  [Using (1) and (2)]

= a2b2 + a2c2 + a2c2 + b2c2 + b2c2 + d2a2 + d2b2 + d2b2 + d2c2

= a2b2 + a2c2 + a2d2 + b2 × b2 + b2c2 + b2d2 + c2b2 + c2 × c2 + c2d2

[Using (2) and (3) and rearranging terms]

= a2(b2 + c2 + d2) + b2(b2 + c2 + d2) + c2(b2 + c2 + d2)

= (a2 + b2 + c2) (b2 + c2 + d2)

= L.H.S

L.H.S. = R.H.S

(a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2

Solution 26
Solution 27
Solution 28

Solution 29

Solution 30
Solution 31
Solution 32

Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7

Solution 8
Solution 9
Solution 10

## Chapter 9 - Sequences and Series Exercise Misc. Ex.

Solution 1
Solution 2
Solution 3
Solution 4

Solution 5

Solution 6
Solution 7
Solution 8
Solution 9
Solution 10

Solution 11
Solution 12
Solution 13
Solution 14
Solution 15

Solution 16
Solution 17
Solution 18

Solution 19

Solution 20

Solution 21

Solution 22
Solution 23

Solution 24
Solution 25
Solution 26

Solution 27

Solution 28

Solution 29
Solution 30
Solution 31
Solution 32

### STUDY RESOURCES

REGISTERED OFFICE : First Floor, Empire Complex, 414 Senapati Bapat Marg, Lower Parel, Mumbai - 400013, Maharashtra India.