CLASS 10 MATH NCERT SOLUTIONS FOR CHAPTER – 5 Arithmetic Progressions Ex – 5.1

Arithmetic Progressions

Question 1.
In which of the following situations, does the list of numbers involved make an arithmetic progression and why?

(i) The taxi fare after each km when the fare is ₹ 15 for the first km and ₹ 8 for each additional km.

(ii) The amount of air present in a cylinder when a vacuum pump removes \frac { 1 }{ 4 } of the air remaining in the cylinder at a time.

(iii) The cost of digging a well after every metre of digging, when it costs ₹ 150 for the first metre and rises by ₹ 50 for each subsequent metre.

(iv) The amount of money in the account every year, when ₹ 10000 is deposited at compound interest at 8% per annum.

Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 1
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 2

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 3

Question 2.
Write first four terms of the AP, when the first term a and the common difference d are given as follows:

(i) a = 10, d = 10
(ii) a = -2, d = 0
(iii) a = 4, d = -3
(iv) a = -1, d = \frac { 1 }{ 2 }
(v) a = -1.25, d = -0.25

Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 4
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 5

Question 3.
For the following APs, write the first term and the common difference:

(i) 3, 1, -1, -3, ……
(ii) -5, -1, 3, 7, ……
(iii) \frac { 1 }{ 3 } , \frac { 5 }{ 3 } , \frac { 9 }{ 3 }\frac { 13 }{ 3 } , ……..
(iv) 0.6, 1.7, 2.8, 3.9, …….

Solution:
let a be the first item and d the common difference, then:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 6

Question 4.
Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.

(i) 2, 4, 8, 16, …….
(ii) 2, \frac { 5 }{ 2 } , 3, \frac { 7 }{ 2 } , …….
(iii) -1.2, -3.2, -5.2, -7.2, ……
(iv) -10, -6, -2,2, …..
(v) 3, 3 + \sqrt { 2 } , 3 + 2\sqrt { 2 } , 3 + 3\sqrt { 2 } , …..
(vi) 0.2, 0.22, 0.222, 0.2222, ……
(vii) 0, -4, -8, -12, …..
(viii) \frac { -1 }{ 2 } , \frac { -1 }{ 2 } , \frac { -1 }{ 2 } , \frac { -1 }{ 2 } , …….
(ix) 1, 3, 9, 27, …….
(x) a, 2a, 3a, 4a, …….
(xi) a, a2, a3, a4, …….
(xii) \sqrt { 2 } \sqrt { 8 } \sqrt { 18 } \sqrt { 32 } , …..
(xiii) \sqrt { 3 } \sqrt { 6 } \sqrt { 9 } \sqrt { 12 } , …..
(xiv) 12, 32, 52, 72, ……
(xv) 12, 52, 72, 73, ……

Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 7
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 8i

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 8
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 9

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 10
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 11

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 12
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 13

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 14