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 

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