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Page 1
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
1
Exercise 5.2
Question 1:
Fill in the blanks in the following table, given that a is the first term, d
the common difference and an the n
th
term of the A.P.
a d n an
I 7 3 8 …...
II - 18 ….. 10 0
III ….. - 3 18 - 5
IV - 18.9 2.5 ….. 3.6
V 3.5 0 105 …..
Answer 1:
I. a = 7, d = 3, n = 8, an = ?
We know that,
For an A.P. an = a + (n - 1) d
= 7 + (8 - 1) 3
= 7 + (7) 3
= 7 + 21 = 28
Hence, an = 28
II. Given that a = -18, n = 10, an = 0, d = ?
We know that,
an = a + (n - 1) d
0 = - 18 + (10 - 1) d
18 = 9d
Page 2
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
1
Exercise 5.2
Question 1:
Fill in the blanks in the following table, given that a is the first term, d
the common difference and an the n
th
term of the A.P.
a d n an
I 7 3 8 …...
II - 18 ….. 10 0
III ….. - 3 18 - 5
IV - 18.9 2.5 ….. 3.6
V 3.5 0 105 …..
Answer 1:
I. a = 7, d = 3, n = 8, an = ?
We know that,
For an A.P. an = a + (n - 1) d
= 7 + (8 - 1) 3
= 7 + (7) 3
= 7 + 21 = 28
Hence, an = 28
II. Given that a = -18, n = 10, an = 0, d = ?
We know that,
an = a + (n - 1) d
0 = - 18 + (10 - 1) d
18 = 9d
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
2
Hence, common difference, d = 2
III. Given that d = -3, n = 18, an = -5
We know that, an = a + (n - 1) d
-5 = a + (18 - 1) (-3)
-5 = a + (17) (-3)
-5 = a - 51
a = 51 - 5 = 46
Hence, a = 46
IV. a = -18.9, d = 2.5, an = 3.6, n = ?
We know that, an = a + (n - 1) d
3.6 = - 18.9 + (n - 1) 2.5
3.6 + 18.9 = (n - 1) 2.5
22.5 = (n - 1) 2.5
Hence, n = 10
V. a = 3.5, d = 0, n = 105, an = ?
We know that, an = a + (n - 1) d
an = 3.5 + (105 - 1) 0
an = 3.5 + 104 × 0
an = 3.5
Hence, an = 3.5
Page 3
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
1
Exercise 5.2
Question 1:
Fill in the blanks in the following table, given that a is the first term, d
the common difference and an the n
th
term of the A.P.
a d n an
I 7 3 8 …...
II - 18 ….. 10 0
III ….. - 3 18 - 5
IV - 18.9 2.5 ….. 3.6
V 3.5 0 105 …..
Answer 1:
I. a = 7, d = 3, n = 8, an = ?
We know that,
For an A.P. an = a + (n - 1) d
= 7 + (8 - 1) 3
= 7 + (7) 3
= 7 + 21 = 28
Hence, an = 28
II. Given that a = -18, n = 10, an = 0, d = ?
We know that,
an = a + (n - 1) d
0 = - 18 + (10 - 1) d
18 = 9d
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
2
Hence, common difference, d = 2
III. Given that d = -3, n = 18, an = -5
We know that, an = a + (n - 1) d
-5 = a + (18 - 1) (-3)
-5 = a + (17) (-3)
-5 = a - 51
a = 51 - 5 = 46
Hence, a = 46
IV. a = -18.9, d = 2.5, an = 3.6, n = ?
We know that, an = a + (n - 1) d
3.6 = - 18.9 + (n - 1) 2.5
3.6 + 18.9 = (n - 1) 2.5
22.5 = (n - 1) 2.5
Hence, n = 10
V. a = 3.5, d = 0, n = 105, an = ?
We know that, an = a + (n - 1) d
an = 3.5 + (105 - 1) 0
an = 3.5 + 104 × 0
an = 3.5
Hence, an = 3.5
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
3
Question 2:
Choose the correct choice in the following and justify
(i). 30
th
term of the A.P: 10, 7, 4, …, is
(A). 97 (B). 77 (C). - 77 (D). - 87
(ii). 11
th
term of the A.P. is
(A). 28 (B). 22 (C). - 38 (D).
Answer 2:
(i) Given that
A.P. 10, 7, 4, …
First term, a = 10
Common difference, d = a2 - a1 = 7 - 10 = -3
We know that, an = a + (n - 1) d
a30 = 10 + (30 - 1) (-3)
a30 = 10 + (29) (-3)
a30 = 10 - 87 = -77
Hence, the correct answer is C.
(ii) Given that, A.P.
First term a = -3
Common difference, d = a2 - a1
Page 4
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
1
Exercise 5.2
Question 1:
Fill in the blanks in the following table, given that a is the first term, d
the common difference and an the n
th
term of the A.P.
a d n an
I 7 3 8 …...
II - 18 ….. 10 0
III ….. - 3 18 - 5
IV - 18.9 2.5 ….. 3.6
V 3.5 0 105 …..
Answer 1:
I. a = 7, d = 3, n = 8, an = ?
We know that,
For an A.P. an = a + (n - 1) d
= 7 + (8 - 1) 3
= 7 + (7) 3
= 7 + 21 = 28
Hence, an = 28
II. Given that a = -18, n = 10, an = 0, d = ?
We know that,
an = a + (n - 1) d
0 = - 18 + (10 - 1) d
18 = 9d
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
2
Hence, common difference, d = 2
III. Given that d = -3, n = 18, an = -5
We know that, an = a + (n - 1) d
-5 = a + (18 - 1) (-3)
-5 = a + (17) (-3)
-5 = a - 51
a = 51 - 5 = 46
Hence, a = 46
IV. a = -18.9, d = 2.5, an = 3.6, n = ?
We know that, an = a + (n - 1) d
3.6 = - 18.9 + (n - 1) 2.5
3.6 + 18.9 = (n - 1) 2.5
22.5 = (n - 1) 2.5
Hence, n = 10
V. a = 3.5, d = 0, n = 105, an = ?
We know that, an = a + (n - 1) d
an = 3.5 + (105 - 1) 0
an = 3.5 + 104 × 0
an = 3.5
Hence, an = 3.5
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
3
Question 2:
Choose the correct choice in the following and justify
(i). 30
th
term of the A.P: 10, 7, 4, …, is
(A). 97 (B). 77 (C). - 77 (D). - 87
(ii). 11
th
term of the A.P. is
(A). 28 (B). 22 (C). - 38 (D).
Answer 2:
(i) Given that
A.P. 10, 7, 4, …
First term, a = 10
Common difference, d = a2 - a1 = 7 - 10 = -3
We know that, an = a + (n - 1) d
a30 = 10 + (30 - 1) (-3)
a30 = 10 + (29) (-3)
a30 = 10 - 87 = -77
Hence, the correct answer is C.
(ii) Given that, A.P.
First term a = -3
Common difference, d = a2 - a1
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
4
We know that,
Hence, the answer is B.
Question 3:
In the following APs find the missing term in the boxes
(i)
(ii)
(iii)
(iv)
(v)
Answer 3:
(i)
For this A.P., a = 2 and a3 = 26
Page 5
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
1
Exercise 5.2
Question 1:
Fill in the blanks in the following table, given that a is the first term, d
the common difference and an the n
th
term of the A.P.
a d n an
I 7 3 8 …...
II - 18 ….. 10 0
III ….. - 3 18 - 5
IV - 18.9 2.5 ….. 3.6
V 3.5 0 105 …..
Answer 1:
I. a = 7, d = 3, n = 8, an = ?
We know that,
For an A.P. an = a + (n - 1) d
= 7 + (8 - 1) 3
= 7 + (7) 3
= 7 + 21 = 28
Hence, an = 28
II. Given that a = -18, n = 10, an = 0, d = ?
We know that,
an = a + (n - 1) d
0 = - 18 + (10 - 1) d
18 = 9d
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
2
Hence, common difference, d = 2
III. Given that d = -3, n = 18, an = -5
We know that, an = a + (n - 1) d
-5 = a + (18 - 1) (-3)
-5 = a + (17) (-3)
-5 = a - 51
a = 51 - 5 = 46
Hence, a = 46
IV. a = -18.9, d = 2.5, an = 3.6, n = ?
We know that, an = a + (n - 1) d
3.6 = - 18.9 + (n - 1) 2.5
3.6 + 18.9 = (n - 1) 2.5
22.5 = (n - 1) 2.5
Hence, n = 10
V. a = 3.5, d = 0, n = 105, an = ?
We know that, an = a + (n - 1) d
an = 3.5 + (105 - 1) 0
an = 3.5 + 104 × 0
an = 3.5
Hence, an = 3.5
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
3
Question 2:
Choose the correct choice in the following and justify
(i). 30
th
term of the A.P: 10, 7, 4, …, is
(A). 97 (B). 77 (C). - 77 (D). - 87
(ii). 11
th
term of the A.P. is
(A). 28 (B). 22 (C). - 38 (D).
Answer 2:
(i) Given that
A.P. 10, 7, 4, …
First term, a = 10
Common difference, d = a2 - a1 = 7 - 10 = -3
We know that, an = a + (n - 1) d
a30 = 10 + (30 - 1) (-3)
a30 = 10 + (29) (-3)
a30 = 10 - 87 = -77
Hence, the correct answer is C.
(ii) Given that, A.P.
First term a = -3
Common difference, d = a2 - a1
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
4
We know that,
Hence, the answer is B.
Question 3:
In the following APs find the missing term in the boxes
(i)
(ii)
(iii)
(iv)
(v)
Answer 3:
(i)
For this A.P., a = 2 and a3 = 26
Mathematics
(www.tiwariacademy.com)
(Chapter – 5) (Arithmetic Progressions)
(Class – X)
www.tiwariacademy.com
5
We know that, an = a + (n - 1) d
a3 = 2 + (3 - 1) d
26 = 2 + 2d
24 = 2d d = 12
a2 = 2 + (2 - 1) 12
= 14
Therefore, 14 is the missing term.
(ii)
For this A.P., a2 = 13 and a4 = 3
We know that, an = a + (n - 1) d
a2 = a + (2 - 1) d
13 = a + d …………………………(I)
a4 = a + (4 - 1) d
3 = a + 3d ………………………..(II)
On subtracting (I) from (II), we obtain -10 = 2d
d = -5
From equation (I), we obtain
13 = a + (-5)
a = 18
a3 = 18 + (3 - 1) (-5)
= 18 + 2 (-5) = 18 - 10 = 8
Therefore, the missing terms are 18 and 8 respectively.
(iii)
For this A.P.,
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FAQs on NCERT Solutions, Exercise 5.2, Arithmetic Progression, Class 10 (Mathematics)
| 1. What is an arithmetic progression? |  |
Ans. An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference.
| 2. How can we find the nth term of an arithmetic progression? | |
Ans. To find the nth term of an arithmetic progression, we use the formula:
nth term = first term + (n-1) * common difference
Where the first term is the initial term of the sequence and the common difference is the difference between any two consecutive terms.
| 3. Can an arithmetic progression have a negative common difference? | |
Ans. Yes, an arithmetic progression can have a negative common difference. In an arithmetic progression, the common difference can be either positive or negative. A negative common difference indicates that the terms of the progression are decreasing.
| 4. How can we find the sum of the first 'n' terms of an arithmetic progression? | |
Ans. The sum of the first 'n' terms of an arithmetic progression can be found using the formula:
Sum = (n/2) * (first term + last term)
Where 'n' is the number of terms, the first term is the initial term of the sequence, and the last term is the nth term of the sequence.
| 5. Can an arithmetic progression have a common difference of zero? | |
Ans. Yes, an arithmetic progression can have a common difference of zero. In such a case, all the terms of the progression will be the same, resulting in a constant sequence.
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