NCERT Solutions for Class 10 Maths Chapter 5 - Arithmetic Progressions

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Chapter 5 - Arithmetic Progressions Exercise Ex. 5.1

Solution 1

Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

Solution 2
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 3
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 4
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

Chapter 5 - Arithmetic Progressions Exercise Ex. 5.2

Solution 1
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 2

We have to find the 30th term and 11th term in I and II respectively.Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

Solution 3
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 4
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 5
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 6
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 7
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 8
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 9
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 10
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 11
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 12
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 13
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 14
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 15
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 16
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 17

Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

Solution 18
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 19
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 20
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

Chapter 5 - Arithmetic Progressions Exercise Ex. 5.3

Solution 1

(i)     2, 7, 12 ,…, to 10 terms

For this AP,

a = 2

d = a2a1 = 7 – 2 = 5 

n = 10

We know that,

Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

(ii)     –37, –33, –29 ,…, to 12 terms

For this AP,

a = –37

d = a2a1 = (–33) – (–37)

 = – 33 + 37 = 4 

n = 12

We know that,


Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

(iii)   0.6, 1.7, 2.8 ,…, to 100 terms

For this AP,

a = 0.6

d = a2a1 = 1.7 – 0.6 = 1.1  

n = 100

We know that,

Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions


 


Solution 2
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 3
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 4
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 5
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 6
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 7

Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

Solution 8
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 9
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 10

(i)

Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

(ii)

Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

Solution 11
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 12
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 13
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 14
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 15
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 16
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 17
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 18
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 19
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 20

In a potato race, a bucket is placed at the starting point, which is 5m from the first potato and other potatoes are placed 3m apart in a straight line. There are ten potatoes in the line.

So, we get the series as

5, 8, 11, 14, ........ 

Here, a= 5 and  d = 8 - 5 = 11 - 8= 3

the difference between the two consecutive terms are same.

So, this is an arithmetic Progression.

According to the condition, we get the series as

5 + 5 , 8 + 8, 11 + 11, .....

10, 16, 22, ..............

Here a = 10 and d = 16 - 10 = 6

the difference between the two consecutive terms are same.

So, this is an arithmetic Progression.

The total distance the competitor has to run is given by,

Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

Therefore the total distance the competitor has to run is 370 m.

Chapter 5 - Arithmetic Progressions Exercise Ex. 5.4

Solution 1
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 2
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 3
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions
Solution 4

The number of houses was 1, 2, 3, ..... 49.

It can be observed that the number of houses are in an AP having a as 1 and d also as 1.

Let us assume that the number of xth house was like this.

We know that,

Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

Sum of number of houses preceding xth house = Sx-1 

Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

Sum of number of houses preceding xth house = S49 - Sx 

Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions

However, the house numbers are positive integers.

The value of x will be 35 only.

Therefore, house number 35 is such that the sum of the numbers of houses preceding

the house numbered 35 is equal to the sum of the numbers of the houses following it.

Solution 5
Ncert Solutions Cbse Class 10 Mathematics Chapter - Arithmetic Progressions