Practice Set 3.1
- 2, 4, 6, 8, . . . Which of the following sequences are A.P. ? If they are A.P. find…
- 2 , 5/2 , 3 , 7/3 , Which of the following sequences are A.P. ? If they are A.P. find…
- - 10, - 6, - 2, 2, . . . Which of the following sequences are A.P. ? If they are A.P.…
- 0.3, 0.33, .0333, . . . Which of the following sequences are A.P. ? If they are A.P.…
- 0, - 4, - 8, - 12, . . . Which of the following sequences are A.P. ? If they are A.P.…
- - 1/5 , - 1/5 , - 1/5 , l Which of the following sequences are A.P. ? If they are A.P.…
- 3 , 3 + root 2 , 3+2 root 2 , 3+3 root 2 , l Which of the following sequences are A.P.…
- 127, 132, 137, . . . Which of the following sequences are A.P. ? If they are A.P. find…
- a = 10, d = 5 Write an A.P. whose first term is a and common difference is d in each…
- a = - 3, d = 0 Write an A.P. whose first term is a and common difference is d in each…
- a = - 7 , d = 1/2 Write an A.P. whose first term is a and common difference is d in…
- a = - 1.25, d = 3 Write an A.P. whose first term is a and common difference is d in…
- a = 6, d = - 3 Write an A.P. whose first term is a and common difference is d in each…
- a = - 19, d = - 4 Write an A.P. whose first term is a and common difference is d in…
- 5, 1, - 3, - 7, . . . Find the first term and common difference for each of the A.P.…
- 0.6, 0.9, 1.2, 1.5, . . . Find the first term and common difference for each of the…
- 127, 135, 143, 151, . . . Find the first term and common difference for each of the…
- 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 
