# RD Sharma Solution Class 11 Mathematics Chapter 19 Arithmetic Progressions

## Chapter 19 – Arithmetic Progressions Exercise Ex. 19.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Find the first four terns of the sequence defined by a1
= 3 and, an = 3an– 1 + 2, for all n > 1

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

## Chapter 19 – Arithmetic Progressions Exercise Ex. 19.4

Question 1

Solution 1

( vii )

Question 2

Solution 2

Question 3

Solution 3

Question 4
Solution 4
Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Find the rth term of an A.P., the sum of whose first n
terms is 3n2 + 2n.

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21
Solution 21
Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

## Chapter 19 – Arithmetic Progressions Exercise Ex. 19.5

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Show that x2 + xy + y2, z2
+ zx + x2 and y2 + yz + z2 are consecutive
terms of an A.P., if x, y and z are in A.P.

Solution 10

## Chapter 19 – Arithmetic Progressions Exercise Ex. 19.6

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

Solution 9

## Chapter 19 – Arithmetic Progressions Exercise Ex. 19.7

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10
Solution 10
Question 11
Solution 11
Question 12

A carpenter was hired to build 192 window frames. The
first day he made five frames and each day thereafter he made two more frames
than he made the day before. How many days did it take him to finish the job?

Solution 12

Question 13

We know that the sum of the interior angles of a
triangle is 180o. Show that the sums of the interior angles of
polygons with 3, 4, 5, 6,…. sides form an arithmetic progression. Find the
sum of the interior angles for a 21 sided polygon.

Solution 13

Question 14

In a potato race 20 potatoes are placed in a line at
intervals of 4 meters with the first potato 24 meters from the starting
point. A contestant is required to bring the potatoes back to the starting
place one at a time. How far would he run in bringing back all the potatoes?

Solution 14

Question 15

A man accepts a position with an initial salary of Rs. 5200 per month.
It is understood that he will receive an automatic increase of
Rs. 320 in the very
next month and each month thereafter.

i. Find his salary for the tenth month.

Solution 15

Question 16

A man accepts a position with an initial salary of Rs. 5200 per month.
It is understood that he will receive an automatic increase of
Rs. 320 in the very
next month and each month thereafter.

What is his total earnings during the first year?

Solution 16

Question 17

A man saved Rs. 66000 in 20
years. In each succeeding year after the first year he saved
Rs. 200 more then
what he saved in the previous year. How much did he save in the first year?

Solution 17

Question 18

In a cricket team tournament 16 teams participated. A
sum of
Rs. 8000 is to be awarded among themselves as prize money.
If the last place team is awarded
Rs. 275 in prize
money and the award increases by the same amount for successive finishing
places, how much amount will the first place team receive?

Solution 18

## Chapter 19 – Arithmetic Progressions Exercise Ex. 19VSAQ

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

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