NCERT Class Solutions
  • Home
  • 9th Solutions
    • Maths Solutions
    • Science Solutions
  • 10th Solutions
    • Science Solutions
    • Maths Solutions
    • Social Science Solutions
    • English Solutions
    • Hindi Solutions
    • Sanskrit Solutions
  • NCERT Books
    • Class 10 Books PDF
  • About Us
    • Write for Us
    • Contact Us
    • Privacy Policy
    • Disclaimer
  • MP Board Solutions
No Result
View All Result
  • Home
  • 9th Solutions
    • Maths Solutions
    • Science Solutions
  • 10th Solutions
    • Science Solutions
    • Maths Solutions
    • Social Science Solutions
    • English Solutions
    • Hindi Solutions
    • Sanskrit Solutions
  • NCERT Books
    • Class 10 Books PDF
  • About Us
    • Write for Us
    • Contact Us
    • Privacy Policy
    • Disclaimer
  • MP Board Solutions
No Result
View All Result
NCERT Class Solutions
No Result
View All Result
Home Class 10th Solutions 10th Maths

NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1

by Sudhir
December 28, 2021
in 10th Maths, Class 10th Solutions
Reading Time: 10 mins read
0
NCERT Class 10th Maths Solutions
0
VIEWS
Share on FacebookShare on Twitter

In this post, we will share NCERT Class 10th Maths Book Solutions Chapter 5 Arithmetic Progressions Ex 5.1. These solutions are based on new NCERT Syllabus.

NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1

NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1

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 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:
(i) Let us consider, the first term
(T1) Fare for the first 1 km = ₹ 15
Since, the taxi fare beyond the first 1 km is ₹ 8 for each additional km.
∴ Fare for 2 km = ₹ 15 + 1 × ₹ 8
T2 = a + 8 [where a = 15]
Fare for 3 km = ₹ 15 + 2 × ₹ 8
⇒ T3 = a + 16
Fare for 4 km= ₹ 15 + 3 × ₹ 8
⇒ T4 = a + 24
Fare for 5 km = ₹ 15 + 4 × ₹ 8
⇒ T5 = a + 32
Fare for n km = ₹ 15 + (n – 1)8
⇒ Tn = a + (n – 1)8
We see that above terms form an AP with common difference 8.

(ii) Let the amount of air present in the cylinder be x
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 1
The above terms are not in A.P.

(iii) Here, the cost of digging for first 1 metre = ₹ 150
The cost of digging for first 2 metres = ₹ 150 + ₹ 50 = ₹ 200
The cost of digging for first 3 metres = ₹ 150 + (₹ 50) × 2 = ₹ 250
The cost of digging for first 4 metres = ₹ 150 + (₹ 50) × 3 = ₹ 300
∴ The terms are: 150, 200, 250, 300,…..
Since, 200 – 150 = 50 and 250 – 200 = 50
(200 – 150) (250 – 200) = 50
∴ The above terms form an AP with common difference 50.

(iv)
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 2
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 3

NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1

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 = 1/2
(y) a = -1.25, d = -0.25
Solution:
(i) ∵ Tn = a + (n – 1)d
∴ For a = 10 and d = 10, we have:
T1 =10 + (1 – 1) × 10 = 10 + 0 = 10
T2 = 10 + (2 – 1) × 10 = 10 + 10 – 20
T3 = 10 + ( 3 – 1) × 10 = 10 + 20 = 30
T4 = 10 + (4 – 1) × 10 = 10 + 30 = 40
Thus, the first four terms are:
10, 20, 30, 40

(ii) ∵ Tn = a + (n – 1)d
∴ For a = -2 and d = 0,we have:
T1 = -2 + (1 – 1) × 0 = -2 + 0 = -2
T2 = -2 + (2 – 1) × 0 = -2 + 0 = -2
T3 = -2 + (3 – 1) × 0= -2 + 0 = -2
T4 = -2 + (4 – 1) × 0 = -2 + 0 = -2
∴ Thus, the first four terms are: -2, -2, -2, -2

(iii) ∵ Tn = a + (n – 1)d
For a = 4 and d = -3, we have:
T1 = 4 + (1 – 1) × (-3) = 4 + 0 = 4
T2 = 4 + (2 – 1) × (-3) = 4 + (-3) = 1
T3 = 4 + (3 – 1) × (-3) = 4 + (-6) = -2
T4 = 4 + (4 – 1) × (-3) = 4 + (-9) = -5
Thus, the first four terms are:
4, 1, -2, -5

(iv)
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 4

(v) ∵ Tn = a + (n – 1)d
∴ For a = -1.25 and d = -0.25, we have
T1 = -1.25 + (1 – 1) × (-0.25) = -1.25 + 0
= -1.25
T2 = -1.25 + (2 – 1) × (-0.25) = -1.25 + (-0.25) = -1.50
T3 = -1.25 + (3 – 1) × (-0.25) = -1.25 + (-0.50) = -1.75
T4 = -1.25 + (4 – 1) × (-0.25) = -1.25 + (-0.75) = -2.0

NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1

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) \(\frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3}, \ldots .\)
(iv) 0.6, 1.7, 2.8, 3.9, …..
Solution:
(i) We have : 3, 1, -1, -3, …
⇒ T1 ⇒ 3 = a = 3
T2 = 1, T3= -1, T4= -3
∴ T2 – T1 = 1 – 3 = -2
T4 = T3 = -3 – (-1) = -3 + 1 = -2 ⇒ d = -2

(ii) We have : -5, -1, 3, 7,….
⇒ T1 = -5 ⇒ a = -5, T2 = -1, T3 = 3, T4 = 7
∴ T2 – T1 = -1 – (-5) = -1 + 5 = 4
and T4 – T3 = 7 – 3 = 4 ⇒ d = 4
Thus a = -5, d = 4

(iii)
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 5

NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1

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) \(3,3+\sqrt{2}, 3+2 \sqrt{2}, 3+3 \sqrt{2}, \ldots\)
(vi) 0.2, 0.22, 0.222, 0.2222, ….
(vii) 0, -4, -8, -12,
(ix) 1, 3, 9, 27, …..
(x) o, 2a, 3a, 4a,…
(xi) a, a2, a3, a4,….
(xii) \(\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, \dots\)
(xiii) \(\sqrt{3}, \sqrt{6}, \sqrt{9}, \sqrt{12}, \dots .\)
(xiv) 12, 32, 52, 72, ….
(xv) 12, 52, 72, 73, …..
Solution:
(i)
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 6
∴ The given numbers do not form an AP

(ii)
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 7

(iii) We have : -1.2, -3.2, -5.2, -7.2,
∴ T1 = -1.2, T2 = -3.2, T3 = -5.2, T4 = -7.2
T2 – T1 = -3.2 + 1.2 = -2
T3 – T2 = -5.2 + 3.2 = -2
T4 – T3 = -7.2 + 5.2 = -2
∵ T2 – T1 = T3 – T2 = T4 – T3 = -2 d = -2
∴ The given numbers form an AP such that d = -2.
Now, T5 = T4 + (-2) = -7.2 + (-2) = -9.2,
T6 = T5 + (-2) = -9.2 + (-2) = -11.2 and
T7 = T6 + (-2) = -11.2 + (-2) = -13.2
Thus, d = -2 and T5 = -9.2, T5 = -11.2 and T6 = -13.2

(iv) We have : -10, -6, -2, 2,
T1 = -10, T2 = -6, T3 = -2, T4 = 2
T2 – T1 = -6 + 10 = 4
T3 – T2 = -2 + 6 = 4
T4 – T3 = 2 + 2 = 4
∵ T2 – T1 = T3 – T2 = T4 – T3 = 4 ⇒ d = 4
∴ The given numbers form an AP Now, T5 = T4 + 4 = 2 + 4 = 6,
T6 = T5 + 4 = 6 + 4 = 10,
T7 = T6 + 4 = 10 + 4 = 14
Thus, d = 4 and T5 = 6, T6 = 10, T7 = 14

(v) We have :
3, 3 + \(\sqrt{2}\), 3 + 2\(\sqrt{2}\), 3 + 3\(\sqrt{2}\),….
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 8

(vi) We have : 0.2, 0.22, 0.222, 0.2222,….
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 9
∴ The given numbers do not form an AP

(vii) We have : 0, – 4, – 8, – 12,
∴ T1 = 0, T2 = -4, T3 = -8, T4 = -12 T2 – T1 = -4 – 0 = -4
T3 – T2 = – 8 + 4 = – 4
T4 – T3 = -12 + 8 = -4
∴ T2 – T1 = T3 – T2 = T4 – T3 = -4 ⇒ d = -4
∴ The given numbers form an AP
Now, T5 = T4 + (- 4) = -12 + (- 4) = -16
T6 = T5 + (-4) = -16 + (-4)= -20
T7 = T6 + (- 4) = -20 + (- 4) = -24
Thus, d = – 4 and T5 = -16, T6 = -20,
T7 = -24.

(viii)
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 10
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 11

(ix) We have, 1, 3, 9, 27,….
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 12

(x) We have : a, 2a, 3a, 4a,
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 13

(xi)
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 14

(xii)
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 15
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 16

(xiii)
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 17

(xiv)
We have : 12, 32, 52, 72,….
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 18

(xv) We have : 12 , 52, 72, 72,….
NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.1 19

Previous Post

NCERT Class 10th Maths Solutions Chapter 4 द्विघात समीकरण Ex 4.4

Next Post

NCERT Class 10th Maths Solutions Chapter 5 Arithmetic Progressions Ex 5.3

Related

How to Get Full Marks in Maths Class 10
Class 10th Solutions

How to Get Full Marks in Maths Class 10

May 16, 2022
9
NCERT Class 10th English Solutions
10th English

Active and Passive Voice Examples with Answers, Rules in Hindi – Easy English Grammar

April 16, 2022
13
NCERT Class 10th Hindi Solutions
10th Hindi

कन्यादान Class 10 MCQs Questions with Answers

February 9, 2022
29
NCERT Class 10th Hindi Solutions
10th Hindi

छाया मत छूना Class 10 MCQs Questions with Answers

February 9, 2022
42

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Recent

How to Get Full Marks in Maths Class 10

How to Get Full Marks in Maths Class 10

May 16, 2022
9

Tenses – English Grammar CBSE Class 10

April 25, 2022
11
NCERT Class 10th English Solutions

Active and Passive Voice Examples with Answers, Rules in Hindi – Easy English Grammar

April 16, 2022
13

Categories

  • Books
    • Class 10 Books PDF
  • Class 10th Solutions
    • 10th English
    • 10th Hindi
    • 10th Maths
    • 10th Sanskrit
    • 10th Science
    • 10th Social Science
  • Class 9th Solutions
    • 9th Maths
    • 9th Science
  • MP Board
  • Uncategorized
NCERT Class Solutions

We provide NCERT Solutions

NCERT Class Solutions App Play Store

Follow us

Browse by Category

  • Books
    • Class 10 Books PDF
  • Class 10th Solutions
    • 10th English
    • 10th Hindi
    • 10th Maths
    • 10th Sanskrit
    • 10th Science
    • 10th Social Science
  • Class 9th Solutions
    • 9th Maths
    • 9th Science
  • MP Board
  • Uncategorized

© 2021 NCERT Class Solutions.

No Result
View All Result
  • Home
  • 9th Solutions
    • Maths Solutions
    • Science Solutions
  • 10th Solutions
    • Science Solutions
    • Maths Solutions
    • Social Science Solutions
    • English Solutions
    • Hindi Solutions
    • Sanskrit Solutions
  • NCERT Books
    • Class 10 Books PDF
  • About Us
    • Write for Us
    • Contact Us
    • Privacy Policy
    • Disclaimer
  • MP Board Solutions

© 2021 NCERT Class Solutions.

This website uses cookies. By continuing to use this website you are giving consent to cookies being used. Visit our Privacy and Cookie Policy.