NCERT Solutions 10th Maths Chapter 5 Arithmetic Progressions Exercise 5.2

NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.2 we will restart our exploration of the world of Arithmetic Progressions. Thus, we are providing you Chapter 5 Arithmetic Progressions NCERT Class 10 Maths Solutions that will help in achieving more marks. You don't have to wander and waste your precious time in finding best CBSE NCERT Solutions.

Exercise 5.2
1. Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P.

Answer
(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
d = 18/9 = 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
(n - 1) = 22.5/2.5
n - 1 = 9
n = 10
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
Choose the correct choice in the following and justify
(i) 30th term of the A.P: 10, 7, 4, …, is
(A) 97 (B) 77 (C) -77 (D.) -87
(ii) 11th term of the A.P. -3, -1/2, ,2 .... is
(A) 28 (B) 22 (C) - 38 (D)
Answer
(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 option C.
(ii) Given that A.P. is -3, -1/2, ,2 ...
First term a = - 3
Common difference, d = a2 - a1 = (-1/2) - (-3)
= (-1/2) + 3 = 5/2
We know that, an = a + (n - 1) d
a11 = 3 + (11 -1)(5/2)
a11 = 3 + (10)(5/2)
a11 = -3 + 25
a11 = 22
Hence, the answer is option B.