## RD Sharma Class 10 Solutions Chapter 5 Arithmetic Progressions VSAQS

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 5 Arithmetic Progressions VSAQS

**Other Exercises**

- RD Sharma Class 10 Solutions Chapter 5 Arithmetic Progressions Ex 5.1
- RD Sharma Class 10 Solutions Chapter 5 Arithmetic Progressions Ex 5.2
- RD Sharma Class 10 Solutions Chapter 5 Arithmetic Progressions Ex 5.3
- RD Sharma Class 10 Solutions Chapter 5 Arithmetic Progressions Ex 5.4
- RD Sharma Class 10 Solutions Chapter 5 Arithmetic Progressions Ex 5.5
- RD Sharma Class 10 Solutions Chapter 5 Arithmetic Progressions Ex 5.6
- RD Sharma Class 10 Solutions Chapter 5 Arithmetic Progressions VSAQS
- RD Sharma Class 10 Solutions Chapter 5 Arithmetic Progressions MCQS

**Answer each of the following questions either in one word or one sentence or as per requirement of the questions :**

**Question 1.**

Define an arithmetic progression.

**Solution:**

A sequence a_{1}, a_{2}, a_{3}, …, an is called an arithmetic progression of then exists a constant d

Such that a_{2} – a_{1} = d, a_{3} – a_{2} = d, ………… a_{n} – a_{n-1} = d

and so on and d is called common difference

**Question 2.**

Write the common difference of an A.P. whose nth term is a_{n} = 3n + 7.

**Solution:**

a_{n} = 3n + 7

a_{1} = 3 x 1 + 7 = 3 + 7 = 10

a_{2} = 3 x 2 + 7 = 6 + 7 = 13

a_{3} = 3 x 3 + 7 = 9 + 7 = 16

d = a_{3} – a_{2} or a_{2} – a_{1} = 16 – 13 = 3 or 13 – 10 = 3

**Question 3.**

Which term of the sequence 114, 109, 104, … is the first negative term ?

**Solution:**

Sequence is 114, 109, 104, …..

Let a_{n} term be negative

**Question 4.**

Write the value of a_{30} – a_{10} for the A.P. 4, 9, 14, 19, …………

**Solution:**

**Question 5.**

Write 5th term from the end of the A.P. 3, 5, 7, 9,…, 201.

**Solution:**

= 3 + 190 = 193

5th term from the end = 193

**Question 6.**

Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.

**Solution:**

**Question 7.**

Write the nth term of an A.P. the sum of whose n terms is S_{n}.

**Solution:**

Sum of n terms = S_{n}

Let a be the first term and d be the common difference a_{n} =S_{n} – S_{n-1}

**Question 8.**

Write the sum of first n odd natural numbers.

**Solution:**

**Question 9.**

Write the sum of first n even natural numbers.

**Solution:**

First n even natural numbers are

2, 4, 6, 8, ……….

Here a = 2, d = 2

**Question 10.**

If the sum of n terms of an A.P. is S_{n} = 3n² + 5n. Write its common difference.

**Solution:**

**Question 11.**

Write the expression for the common difference of an A.P. Whose first term is a and nth term is b.

**Solution:**

First term of an A.P. = a

and a_{n} = a + (n – 1) d = b .

Subtracting, b – a = (n – 1) d

d = \(\frac { b – a }{ n – 1 }\)

**Question 12.**

The first term of an A.P. is p and its common difference is q. Find its 10th term.** [CBSE 2008]**

**Solution:**

First term of an A.P. (a) = p

and common difference (d) = q

a_{10} = a + (n – 1) d

= p + (10 – 1) q = p + 9q

**Question 13.**

For what value of p are 2p + 1, 13, 5p – 3 are three consecutive terms of an A.P.?** [CBSE 2009]**

**Solution:**

**Question 14.**

If \(\frac { 4 }{ 5 }\), a, 2 are three consecutive terms of an A.P., then find the value of a.

**Solution:**

**Question 15.**

If the sum of first p term of an A.P. is ap² + bp, find its common difference.

**Solution:**

**Question 16.**

Find the 9th term from the end of the A.P. 5, 9, 13, …, 185. **[CBSE 2016]**

**Solution:**

Here first term, a = 5

Common difference, d = 9 – 5 = 4

Last term, l = 185

nth term from the end = l – (n – 1) d

9th term from the end = 185 – (9 – 1) 4 = 185 – 8 x 4 = 185 – 32 = 153

**Question 17.**

For what value of k will the consecutive terms 2k + 1, 3k + 3 and 5k – 1 form on A.P.? **[CBSE 2016]**

**Solution:**

(3k + 3) – (2k + 1) = (5k – 1) – (3k + 3)

3k + 3 – 2k – 1 = 5k – 1 – 3k – 3

k + 2 = 2k – 4

2k – k = 2 + 4

k = 6

**Question 18.**

Write the nth term of the A.P.

\(\frac { 1 }{ m }\) , \(\frac { 1 + m }{ m }\) , \(\frac { 1 + 2m }{ m }\) , ……… **[CBSE 2017]**

**Solution:**

Hope given RD Sharma Class 10 Solutions Chapter 5 Arithmetic Progressions VSAQS are helpful to complete your math homework.

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