Arithmetic Progression

NCERT 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 is the nth term of the AP.

Answer:

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

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, a_n = 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, a_n = - 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, a_n = 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, a_n = ?

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

Answer: Answer (C) – 77

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

Answer: Answer (B) 22

Here, a = - 3, d = 5/2 and n = 11

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`