**RD Sharma Class 10 Solutions Chapter 9 Exercise 9.3: **This exercise puts the basic concept of A.P to the test. The nth term of the A.P. and problems of identifying the common difference are thoroughly practised here. Students will find the **RD Sharma Class 10 Solutions** prepared by subject experts at Kopykitab to be a very useful resource for reference and exam preparation. For full solutions to questions, check the **RD Sharma Solutions for Class 10 Maths Chapter 9** Exercise 9.3 PDF provided below.

Table of Contents

## Download RD Sharma Class 10 Solutions Chapter 9 Exercise 9.3 Free PDF

RD Sharma Class 10 Solutions Chapter 9 Exercise 9.3

### Access answers to RD Sharma Solutions Class 10 Maths Chapter 9 Exercise 9.3- Important Question with Answers

Question 1.

For the following arithmetic progressions write the first term a and the common difference d :

(i) -5, -1, 3, 7, …………

(ii) 15 , 35 , 55 , 75 , ……

(iii) 0.3, 0.55, 0.80, 1.05, …………

(iv) -1.1, -3.1, -5.1, -7.1, …………..

Solution:

(i) -5, -1, 3, 7, …………

Question 2.

Write the arithmetic progression when first term a and common difference d are as follows:

(i) a = 4, d = -3

(ii) a = -1, d= 12

(iii) a = -1.5, d = -0.5

Solution:

(i) First term (a) = 4

and common difference (d) = -3

Second term = a + d = 4 – 3 = 1

Third term = a + 2d = 4 + 2 x (-3) = 4 – 6 = -2

Fourth term = a + 3d = 4 + 3 (-3) = 4 – 9 = -5

Fifth term = a + 4d = 4 + 4 (-3) = 4 – 12 = -8

AP will be 4, 1, -2, -5, -8, ……….

Question 3.

In which of the following situations, the sequence of numbers formed will form an A.P.?

(i) The cost of digging a well for the first meter is ₹ 150 and rises by ₹ 20 for each succeeding meter.

(ii) The amount of air present in the cylinder when a vacuum pump removes each time 14 of the remaining in the cylinder.

(iii) Divya deposited ₹ 1000 at compound interest at the rate of 10% per annum. The amount at the end of the first year, second year, third year, …, and so on. [NCERT Exemplar]

Solution:

(i) Cost of digging a well for the first meter = ₹ 150

Cost for the second metre = ₹ 150 + ₹ 20 = ₹ 170

Cost for the third metre = ₹ 170 + ₹ 20 = ₹ 190

Cost for the fourth metre = ₹ 190 + ₹ 20 = ₹ 210

The sequence will be (In rupees)

150, 170, 190, 210, ………..

Which is an A.P.

Whose = 150 and d = 20

(ii) Let air present in the cylinder = 1

(iii) Amount at the end of the 1st year = ₹ 1100

Amount at the end of the 2nd year = ₹ 1210

Amount at the end of 3rd year = ₹ 1331 and so on.

So, the amount (in ₹) at the end of 1st year, 2nd year, 3rd year, … are

1100, 1210, 1331, …….

Here, a_{2} – a_{1} = 110

a_{3} – a_{2} = 121

As, a_{2} – a_{1} ≠ a_{3} – a_{2}, it does not form an AP

Question 4.

Find the common difference and write the next four terms of each of the following arithmetic progressions :

(i) 1, -2, -5, -8, ……..

(ii) 0, -3, -6, -9, ……

(iii) -1, 14 , 32 , ……..

(iv) -1, – 56 , – 23 , ………..

Solution:

Question 5.

Prove that no matter what the real numbers a and b are, the sequence with the nth term a + nb is always an A.P. What is the common difference?

Solution:

an = a + nb

Let n= 1, 2, 3, 4, 5, ……….

a_{1} = a + b

a_{2} = a + 2b

a_{3} = a + 3b

a_{4} = a + 4b

a_{5} = a + 5b

We see that it is an A.P. whose common difference is b and a for any real value of a and b

as a_{2} – a_{1} = a + 2b – a – b = b

a_{3} – a_{2} = a + 3b – a – 2b = b

a_{4} – a_{3} = a + 4b – a – 3b = b

and a_{5} – a_{4} = a + 5b – a – 4b = b

Question 6.

Find out which of the following sequences are arithmetic progressions. For those who are arithmetic progressions, find out the common difference.

Solution:

Question 7.

Find the common difference of the A.P. and write the next two terms :

(i) 51, 59, 67, 75, …….

(ii) 75, 67, 59, 51, ………

(iii) 1.8, 2.0, 2.2, 2.4, …….

(iv) 0, 14 , 12 , 34 , ………..

(v) 119, 136, 153, 170, ………..

Solution:

We have provided complete details of RD Sharma Class 10 Solutions Chapter 9 Exercise 9.3. If you have any queries related to **CBSE** Class 10, feel free to ask us in the comment section below.

## FAQs on RD Sharma Class 10 Solutions Chapter 9 Exercise 9.3

### Is the RD Sharma Class 10 Solutions Chapter 9 Exercise 9.3 available on the Kopykitab website?

Yes, the PDFs of RD Sharma Class 10 Solutions Chapter 9 Exercise 9.3 are available. These solutions are created in a unique method by Kopykitab’s expert faculty.

### What are the key benefits of learning RD Sharma Solutions for Class 10 Maths Chapter 9 Exercise 9.3?

The RD Sharma Class 10 Solutions Chapter 9 Exercise 9.3 answers were quite helpful. This makes it simple to clear any questions about arithmetic progression. Easily answer all of the questions that the Class 10 students have given for exercise.

### Where can I get RD Sharma Class 10 Solutions Chapter 9 Exercise 9.3 Free PDF?

You can get RD Sharma Class 10 Solutions Chapter 9 Exercise 9.3 Free PDF from the above article.