# Arithmetic Progression

## NCERT Exercise 5.2

### Part 1

Question: 1 – Fill in the blanks in the following table, given that a is the first term, d the common difference and an is the nth term of the AP.

(i)738...
(ii)- 18...100
(iii)...- 318- 5
(iv)- 18.92.5...3.6
(v)3.501-5...

Solution:

(i) Given a = 7, d = 3 and n = 8, therefore an = ?

We know that a_n = a + (n – 1)d

Thus, a_n = 7 + (8 – 1)3 = 7 + 21 = 28

(ii) Given a = - 18, n = 10, an = 0, d = ?

We know that a_n = a + (n – 1)d

Thus, 0 = - 18 + (10 – 1)d

Or, 0 = - 18 + 9d

Or, 9d = 18

Or, d = (18)/(9) = 2

(iii) Given d = - 3, n = 18, an = - 5, a = ?

We know that, a_n = a + (n – 1)d

Or, - 5 = a + (18 – 1) (- 3)

Or, - 5 = a – 51

Or, a = - 5 + 51 = 46

(iv) Given a = - 18.9, d = 2.5, an = 3.6, n = ?

We know that, a_n = a + (n – 1)d

Or, 3.6 = – 18.9 + (n – 1)2.5

Or, 2.5(n – 1) = 3.6 + 18.9 = 22.5

Or, n – 1 = (22.5)/(2.5) = 9

Or, n = 9 + 1 = 10

(v) Given a = 3.5, d = 0, n = 105, an = ?

We know that, a_n = a + (n – 1)d

Or, a_n = 3.5 + (104 – 1)0

Or, a_n – 3.5 + 0 = 3.5

Question: 2 – Choose the correct choice in the following and justify:

(i) 30th term of the AP: 10, 7, 4, ……….

(A) 97 (B) 77 (C) – 77 (D) – 87

Here, a = 10, d = – 3 and n = 30

We know that, a_n = a + (n – 1)d

Or, a_(30) = 10 + (30 – 1)(- 3)

= 10 – 87 = - 77

(ii) 11th term of AP: - 3, - ½, 2, ……

(A) 28 (B) 22 (C) – 38 (D) – 48 ½

We know that, a_n = a + (n – 1)d
Or, a_(11) = - 3 + (11 – 1) 5/2
= - 3 + 10 xx 5/2 = - 3 + 25 = 22