CLASS 10 MATH NCERT SOLUTIONS FOR CHAPTER – 5 ARITHMETIC PROGRESSIONS EX – 5.3

Arithmetic Progressions

Question 1.
Find the sum of the following APs:

(i) 2, 7, 12,…… to 10 terms.
(ii) -37, -33, -29, …… to 12 terms.
(iii) 0.6, 1.7, 2.8, ……, to 100 terms.
(iv) \frac { 1 }{ 15 }\frac { 1 }{ 12 }\frac { 1 }{ 10 }, …….., to 11 terms.

Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 48
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 49
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 50

Question 2.
Find the sums given below:

(i) 7 + 10\frac { 1 }{ 2 } + 14 + … + 84
(ii) 34 + 32 + 30 + … + 10
(iii) -5 + (-8) + (-11) + ….. + (-230)

Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 51
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 52
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 53

Question 3.
In an AP:

(i) given a = 5, d = 3, an = 50, find n and Sn.
(ii) given a = 7, a13 = 35, find d and S13.
(iii) given a12 = 37, d = 3, find a and S12.
(iv) given a3 = -15, S10 = 125, find d and a10.
(v) given d = 5, S9 = 75, find a and a9.
(vi) given a = 2, d = 8, Sn = 90, find n and an.
(vii) given a = 8, an = 62, Sn = 210, find n and d.
(viii) given an = 4, d = 2, Sn = -14, find n and a.
(ix) given a = 3, n = 8, S = 192, find d.
(x) given l = 28, S = 144, and there are total 9 terms. Find a.

Solution

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 54
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 55
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 56
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 57
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 58
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 59
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 60

Question 4.
How many terms of AP: 9, 17, 25, … must be taken to give a sum of 636?

Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 61
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 62

Question 5.
The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 63

Question 6.
The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 64

Ex 5.3 Class 10 Maths Question 7.
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 65

Question 8.
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 66

Question 9.
If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 67

Question 10.
Show that a1, a2, ……. an,…… form an AP where an is defined as below:

(i) an = 3 + 4n
(ii) an = 9 – 5n
Also find the sum of the first 15 terms in each case.

Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 68
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 69

Question 11.
If the sum of the first n terms of an AP is 4n – n2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 70
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 71

Question 12.
Find the sum of the first 40 positive integers divisible by 6.

Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 72

Question 13.
Find the sum of the first 15 multiples of 8.

Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 73

Question 14.
Find the sum of the odd numbers between 0 and 50.

Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 74

Question 15.
A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows:

₹ 200 for the first day, ₹ 250 for the second day, ₹ 300 for the third day, etc. the penalty for each succeeding day being ₹ 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?

Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 75

Question 16.
A sum of ₹ 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ 20 less than its preceding prize, find the value of each of the prizes.

Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 76

Question 17.
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, eg. a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?

Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 77

Question 18.
A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm,… as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles?
(Take π = \frac { 22 }{ 7 })
[Hint: Length of successive semicircles is l1, l2, l3, l4, … with centres at A, B, respectively.]

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 78


Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 79

Question 19.
200 logs are stacked in the following manner 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on (see Figure). In how many rows are the 200 logs placed and how many logs are in the top row?

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 80

Solution:
NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 81

Ex 5.3 Class 10 Maths Question 20.
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 82

A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

Solution:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions 83

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