Practice Set 3.1 Arithmetic Progression Class 10th Mathematics Part 1 MHB Solution

Practice Set 3.1

1. 2, 4, 6, 8, . . . Which of the following sequences are A.P. ? If they are A.P. find…
2. 2 , 5/2 , 3 , 7/3 , Which of the following sequences are A.P. ? If they are A.P. find…
3. - 10, - 6, - 2, 2, . . . Which of the following sequences are A.P. ? If they are A.P.…
4. 0.3, 0.33, .0333, . . . Which of the following sequences are A.P. ? If they are A.P.…
5. 0, - 4, - 8, - 12, . . . Which of the following sequences are A.P. ? If they are A.P.…
6. - 1/5 , - 1/5 , - 1/5 , l Which of the following sequences are A.P. ? If they are A.P.…
7. 3 , 3 + root 2 , 3+2 root 2 , 3+3 root 2 , l Which of the following sequences are A.P.…
8. 127, 132, 137, . . . Which of the following sequences are A.P. ? If they are A.P. find…
9. a = 10, d = 5 Write an A.P. whose first term is a and common difference is d in each…
10. a = - 3, d = 0 Write an A.P. whose first term is a and common difference is d in each…
11. a = - 7 , d = 1/2 Write an A.P. whose first term is a and common difference is d in…
12. a = - 1.25, d = 3 Write an A.P. whose first term is a and common difference is d in…
13. a = 6, d = - 3 Write an A.P. whose first term is a and common difference is d in each…
14. a = - 19, d = - 4 Write an A.P. whose first term is a and common difference is d in…
15. 5, 1, - 3, - 7, . . . Find the first term and common difference for each of the A.P.…
16. 0.6, 0.9, 1.2, 1.5, . . . Find the first term and common difference for each of the…
17. 127, 135, 143, 151, . . . Find the first term and common difference for each of the…
18. 1/4 , 3/4 , 5/4 , 7/4 , l Find the first term and common difference for each of the…

Practice Set 3.1

Question 1.

Which of the following sequences are A.P. ? If they are A.P. find the common difference.

2, 4, 6, 8, . . .

Answer:

2, 4, 6, 8, . . .

Here, the first term, a1 = 2

Second term, a2 = 4

a3 = 6

Now, common difference = a2 – a1 = 4 – 2 = 2

Also, a3 – a2 = 6 – 4 = 2

Since, the common difference is same.

Hence the terms are in Arithmetic progression with common difference, d = 2.

Question 2.

Which of the following sequences are A.P. ? If they are A.P. find the common difference.

Answer:

Here, the first term, a1 = 2

Second term, 

Third Term, a3 = 3

Now, common difference = 

Also, 

Since, the common difference is same.

Hence the terms are in Arithmetic progression with common difference, 

Question 3.

Which of the following sequences are A.P. ? If they are A.P. find the common difference.

– 10, – 6, – 2, 2, . . .

Answer:

– 10, – 6, – 2,2, . . .

Here, the first term, a1 = – 10

Second term, a2 = – 6

a3 = – 2

Now, common difference = a2 – a1 = – 6 – ( – 10) = – 6 + 10 = 4

Also, a3 – a2 = – 2 – ( – 6) = – 2 + 6 = 4

Since, the common difference is same.

Hence the terms are in Arithmetic progression with common difference, d = 4.

Question 4.

Which of the following sequences are A.P. ? If they are A.P. find the common difference.

0.3, 0.33, .0333, . . .

Answer:

0.3, 0.33, 0.333,…..

Here, the first term, a1 = 0.3

Second term, a2 = 0.33

a3 = 0.333

Now, common difference = a2 – a1 = 0.33 – 0.3 = 0.03

Also, a3 – a2 = 0.333 – 0.33 = 0.003

Since, the common difference is not same.

Hence the terms are not in Arithmetic progression

Question 5.

Which of the following sequences are A.P. ? If they are A.P. find the common difference.

0, – 4, – 8, – 12, . . .

Answer:

0, – 4, – 8, – 12, . . .

Here, the first term, a1 = 0

Second term, a2 = – 4

a3 = – 8

Now, common difference = a2 – a1 = – 4 – 0 = – 4

Also, a3 – a2 = – 8 – ( – 4) = – 8 + 4 = – 4

Since, the common difference is same.

Hence the terms are in Arithmetic progression with common difference, d = – 4.

Question 6.

Which of the following sequences are A.P. ? If they are A.P. find the common difference.

Answer:

Here, the first term, 

Second term, 

Now, common difference 

Also, 

Since, the common difference is same.

Hence the terms are in Arithmetic progression with common difference, .

Question 7.

Which of the following sequences are A.P. ? If they are A.P. find the common difference.

Answer:

3, 3 + √2, 3 + 2√2, 3 + 3√2, ….

Here, the first term, a1 = 3

Second term, a2 = 3 + √2

a3 = 3 + 2√2

Now, common difference = a2 – a1 = 3 + √2 – 3 = √2

Also, a3 – a2 = 3 + 2√2 –(3 + √2) = 3 + 2√2 – 3 – √2 = √2

Since, the common difference is same.

Hence the terms are in Arithmetic progression with common difference, d = √2 .

Question 8.

Which of the following sequences are A.P. ? If they are A.P. find the common difference.

127, 132, 137, . . .

Answer:

127, 132, 137, . . .

Here, the first term, a1 = 127

Second term, a2 = 132

a3 = 137

Now, common difference = a2 – a1 = 132 – 127 = 5

Also, a3 – a2 = 137 – 132 = 5

Since, the common difference is same.

Hence the terms are in Arithmetic progression with common difference, d = 5.

Question 9.

Write an A.P. whose first term is a and common difference is d in each of the following.

a = 10, d = 5

Answer:

a = 10, d = 5

Let a1 = a = 10

Since, the common difference d = 5

Using formula an + 1 = an + d

Thus, a2 = a1 + d = 10 + 5 = 15

a3 = a2 + d = 15 + 5 = 20

a4 = a3 + d = 20 + 5 = 25

Hence, An A.P with common difference 5 is 10, 15, 20, 25,….

Question 10.

Write an A.P. whose first term is a and common difference is d in each of the following.

a = – 3, d = 0

Answer:

a = – 3, d = 0

Let a1 = a = – 3

Since, the common difference d = 0

Using formula an + 1 = an + d

Thus, a2 = a1 + d = – 3 + 0 = – 3

a3 = a2 + d = – 3 + 0 = – 3

a4 = a3 + d = – 3 + 0 = – 3

Hence, An A.P with common difference 0 is – 3, – 3, – 3, – 3,….

Question 11.

Write an A.P. whose first term is a and common difference is d in each of the following.

Answer:

a = – 7, 

Let a1 = a = – 7

Since, the common difference 

Using formula an + 1 = an + d

Thus, 

Hence, An A.P with common difference  is 

Question 12.

Write an A.P. whose first term is a and common difference is d in each of the following.

a = – 1.25, d = 3

Answer:

a = – 1.25, d = 3

Let a1 = a = – 1.25

Since, the common difference d = 3

Using formula an + 1 = an + d

Thus, a2 = a1 + d = – 1.25 + 3 = 1.75

a3 = a2 + d = 1.75 + 3 = 4.75

a4 = a3 + d = 4.75 + 3 = 7.75

Hence, An A.P with common difference 3 is – 1.25, 1.75, 4.75, 7.75

Question 13.

Write an A.P. whose first term is a and common difference is d in each of the following.

a = 6, d = – 3

Answer:

a = 6, d = – 3

Let a1 = a = 6

Since, the common difference d = – 3

Using formula an + 1 = an + d

Thus, a2 = a1 + d = 6 + ( – 3) = 6 – 3 = 3

a3 = a2 + d = 3 + ( – 3) = 3 – 3 = 0

a4 = a3 + d = 0 + ( – 3) = – 3

Hence, An A.P with common difference – 3 is 6, 3, 0, – 3…

Question 14.

Write an A.P. whose first term is a and common difference is d in each of the following.

a = – 19, d = – 4

Answer:

a = – 19, d = – 4

Let a1 = a = – 19

Since, the common difference d = – 4

Using formula an + 1 = an + d

Thus, a2 = a1 + d = – 19 + ( – 4) = – 19 – 4 = – 23

a3 = a2 + d = – 23 + ( – 4) = – 23 – 4 = – 27

a4 = a3 + d = – 27 + ( – 4) = – 27 – 4 = – 31

Hence, An A.P with common difference – 4 is – 19, – 23, – 27, – 31,….

Question 15.

Find the first term and common difference for each of the A.P.

5, 1, – 3, – 7, . . .

Answer:

5, 1, – 3, – 7, . . .

First term a1 = 5

Second term a2 = 1

Third term a3 = – 3

We know that d = an + 1 – an

Thus, d = a2 – a1 = 1 – 5 = – 4

Hence, the common difference d = – 4 and first term is 5

Question 16.

Find the first term and common difference for each of the A.P.

0.6, 0.9, 1.2, 1.5, . . .

Answer:

0.6, 0.9, 1.2, 1.5, . . .

First term a1 = 0.6

Second term a2 = 0.9

Third term a3 = 1.2

We know that d = an + 1 – an

Thus, d = a2 – a1 = 0.9 – 0.6 = 0.3

Hence, the common difference d = 0.3 and first term is 0.6

Question 17.

Find the first term and common difference for each of the A.P.

127, 135, 143, 151, . . .

Answer:

127, 135, 143, 151, . . .

First term a1 = 127

Second term a2 = 135

Third term a3 = 143

We know that d = an + 1 – an

Thus, d = a2 – a1 = 135 – 127 = 8

Hence, the common difference d = 8 and first term is 127

Question 18.

Find the first term and common difference for each of the A.P.

Answer:

First term 

Second term 

Third term 

We know that d = an + 1 – an

Thus, 

Hence, the common difference  and first term is