Basic terminologies of A.P and its general term calculation are discussed in this exercise. Problems pertaining to these concepts are practised under the exercise 10(A). Students having any doubts regarding solving problems of this exercise can refer toÂ Selina Solutions Concise Maths Class 10Â Chapter 10 Exercise 10(A). Further, the answers to this exercise can be accessed in the Selina Solutions Concise Maths for Class 10 Chapter 10 Arithmetic Progression Exercise 10(A) PDF, which is given in the links below.

## Selina Solutions Concise Maths Class 10 Chapter 10 Arithmetic Progression Exercise 10(A) Download PDF

### Access Selina Solutions Concise Maths Class 10 Chapter 10 Arithmetic Progression Exercise 10(A)

#### Exercise 10(A) Page No: 137

**1. Which of the following sequences are in arithmetic progression?**

**(i)Â 2, 6, 10, 14, â€¦.**

**(ii)Â 15, 12, 9, 6, â€¦.**

**(iii)Â 5, 9, 12, 18, â€¦.**

**(iv) 1/2, 1/3, 1/4, 1/5, â€¦.**

**Solution: **

(i)Â 2, 6, 10, 14, â€¦.

Finding the difference between the terms,

d_{1} = 6 â€“ 2 = 4

d_{2} = 10 – 6 = 4

d_{3 }= 14 â€“ 10 = 4

As d_{1} = d_{2} = d_{3}, the given sequence is in arithmetic progression.

(ii)Â 15, 12, 9, 6, â€¦.

Finding the difference between the terms,

d_{1} = 12 â€“ 15 = -3

d_{2} = 9 – 12 = -3

d_{3 }= 6 â€“ 9 = -3

As d_{1} = d_{2} = d_{3}, the given sequence is in arithmetic progression.

(iii)Â 5, 9, 12, 18, â€¦.

Finding the difference between the terms,

d_{1} = 9 â€“ 5 = 4

d_{2} = 12 – 9 = 3

d_{3 }= 18 â€“ 12 = 6

As d_{1} â‰ d_{2} â‰ d_{3}, the given sequence is not in arithmetic progression.

(iv) 1/2, 1/3, 1/4, 1/5, â€¦.

Finding the difference between the terms,

d_{1} = 1/3 â€“ 1/2 = -1/6

d_{2} = 1/4 â€“ 1/3 = -1/12

d_{3 }= 1/5 â€“ 1/4 = -1/20

As d_{1} â‰ d_{2} â‰ d_{3}, the given sequence is not in arithmetic progression.

**2. The n ^{th}Â term of sequence is (2n – 3), find its fifteenth term.**

**Solution: **

Given, n^{th}Â term of sequence is (2n – 3)

So, the 15^{th} term is when n = 15

t_{15 }= 2(15) â€“ 3 = 30 â€“ 3 = 27

Thus, the 15^{th} term of the sequence is 27.

**3. If theÂ p ^{th}Â term of an A.P. is (2p + 3); find the A.P.**

**Solution: **

Given, p^{th}Â term of an A.P. = (2p + 3)

So, on putting p = 1, 2, 3, â€¦, we have

t_{1} = 2(1) + 3 = 5

t_{2} = 2(2) + 3 = 7

t_{3} = 2(3) + 3 = 9

â€¦..

Hence, the sequence A.P. is 5, 7, 9, â€¦

**4. Find the 24 ^{th}Â term of the sequence:**

**12, 10, 8,Â 6,â€¦â€¦**

**Solution:**

Given sequence,

12, 10, 8,Â 6,â€¦â€¦

The common difference:

10 â€“ 12 = -2

8 â€“ 10 = -2

6 â€“ 8 = -2 â€¦.

So, the common difference(d) of the sequence is -2 and a = 12.

Now, the general term of this A.P. is given by

t_{n} = a + (n – 1)d = 12 + (n – 1)(-2) = 12 â€“ 2n + 2 = 14 â€“ 2n

For 24^{th} term, n = 24

t_{n} = 14 â€“ 2(24) = 14 â€“ 48 = -34

Therefore, the 24^{th} term is -34

**5. Find the 30 ^{th}Â term of the sequence:**

**1/2, 1, 3/2, â€¦â€¦. **

**Solution:**

Given sequence,

1/2, 1, 3/2, â€¦â€¦.

So,

a = Â½

d = 1 â€“ Â½ = Â½

We know that,

t_{n} = a + (n – 1)d

Hence, the 30^{th} term will be

t_{30} = Â½ + (30 – 1)(1/2) = Â½ + 29/2 = 30/2 = 15

Therefore, the 30^{th} term is 15.

**6. Find the 100 ^{th} term of the sequence:**

**âˆš3, 2âˆš3, 3âˆš3, â€¦.**

**Solution: **

Given A.P. is âˆš3, 2âˆš3, 3âˆš3, â€¦.

So,

a = âˆš3

d = 2âˆš3 – âˆš3 = âˆš3

The general term is given by,

t_{n} = a + (n – 1)d

For 100^{th} term

t_{100} = âˆš3 + (100 – 1) âˆš3 = âˆš3 + 99âˆš3 = 100âˆš3

Therefore, the 100^{th} term of the given A.P. is 100âˆš3.

**7. Find the 50 ^{th} term of the sequence: **

**1/n, (n+1)/n, (2n+1)/n, â€¦â€¦**

**Solution: **

Given sequence,

1/n, (n+1)/n, (2n+1)/n, â€¦â€¦

So,

a = 1/n

d = (n+1)/n â€“ 1/n = (n+1-1)/n = 1

Then, the general term is given by

t_{n} = a + (n – 1)d

For 50^{th} term, n = 50

t_{50} = 1/n + (50 – 1)1 = 1/n + 49 = (49n + 1)/n

Hence, the 50^{th} term of the given sequence is (49n + 1)/n.

**8. Is 402Â a term of the sequence: 8, 13, 18, 23,â€¦â€¦â€¦â€¦.?**

**Solution: **

Give sequence, 8, 13, 18, 23,â€¦â€¦â€¦â€¦.

d = 13 â€“ 8 = 5 and a = 8

So, the general term is given by

t_{n} = a + (n – 1)d

t_{n} = 8 + (n – 1)5 = 8 + 5n â€“ 5 = 3 + 5n

Now,

If 402 is a term of the sequence whose n^{th} is given by (3 + 5n) then n must be a non-negative integer.

3 + 5n = 402

5n = 399

n = 399/5

So, clearly n is a fraction.

Thus, we can conclude that 402 is not a term of the given sequence.

**9. Find the common difference and 99 ^{th} term of the arithmetic progression: **

**Solution:**

Given, A.P,

i.e., 31/4, 19/2, 45/4, â€¦â€¦.

So,

a = 31/4

Common difference, d = 19/2 â€“ 31/4 = (38 – 31)/ 4 = 7/4

Then the general term of the A.P

t_{n} = a + (n – 1)d

t_{99} = (31/4) + (99 – 1) x (7/4)

= (31/4) + 93 x (7/4)

= (31/4) + (686 / 4)

= (31 + 686)/ 4

= (717)/ 4

= 179 Â¼

Hence, the 99^{th} term of A.P. is

**10. How many terms are there in the series :**

**(i)Â 4, 7, 10, 13, â€¦â€¦â€¦â€¦,Â 148?**

**(ii)Â 0.5, 0.53, 0.56, â€¦â€¦â€¦â€¦â€¦,Â 1.1?**

**(iii) 3/4, 1, 1 Â¼, â€¦â€¦., 3?**

**Solution: **

(i) Given series, 4, 7, 10, 13, â€¦â€¦â€¦â€¦,Â 148

Here,

a = 4 and d = 7 â€“ 4 = 3

So, the given term is given by t_{n} = 4 + (n – 1)3 = 4 + 3n â€“ 3

t_{n} = 1 + 3n

Now,

148 = 1 + 3n

147 = 3n

n = 147/3 = 49

Thus, there are 49 terms in the series.

(ii) Given series, 0.5, 0.53, 0.56, â€¦â€¦â€¦â€¦â€¦,Â 1.1

Here,

a = 0.5 and d = 0.53 â€“ 0.5 = 0.03

So, the given term is given by t_{n} = 0.5 + (n – 1)0.03 = 0.5 + 0.03n â€“ 0.03

t_{n} = 0.47 + 0.03n

Now,

1.1 = 0.47 + 0.03n

1.1 â€“ 0.47 = 0.03n

n = 0.63/0.03 = 21

Thus, there are 21 terms in the series.

(iii) Given series, 3/4, 1, 1 Â¼, â€¦â€¦., 3

Here,

a = 3/4 and d = 1 â€“ 3/4 = 1/4

So, the given term is given by t_{n} = 3/4 + (n – 1)1/4 = (3 + n â€“ 1)/4

t_{n} = (2 + n)/ 4

Now,

3 = (2 + n)/ 4

12 = 2 + n

n = 10

Thus, there are 10 terms in the series.