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### 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, . . .

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.

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, . . .

– 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, . . .

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, . . .

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.

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.

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, . . .

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

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

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.

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

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

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

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, . . .

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, . . .

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, . . .

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.

First term

Second term

Third term

We know that d = an + 1 – an

Thus,

Hence, the common difference  and first term is