# Choose the correct choice in the following and justify:

i) 30^{th} term of the AP: 10, 7, 4,..., is

a) 97 b) 77 c) - 77 d) - 87

ii) 11^{th} term of the AP: -3, - 1/2, 2,..., is

a) 28 b) 22 c) - 38 d) - \(48{\Large\frac{1}{2}}\)

**Solution:**

i) n^{th} term of an AP is aₙ = a + (n - 1) d

The AP is 10, 7, 4, …

Here, a = 10, n = 30

Common difference, d = a₂ - a₁ = 7 - 10 = - 3

aₙ = a + (n - 1)d

a₃₀ = 10 + (30 - 1)(- 3)

= 10 + (29)(- 3)

= 10 - 87

= - 77

The correct option is c = - 77. Thus, 30^{th} term of the AP is - 77.

ii) The AP is - 3, - 1/2 , 2

a = -3, n = 11

Common difference d = a₂ - a₁

= - 1/2 - (- 3)

= - 1/2 + 3

= (- 1 + 6) / 2

d = 5 / 2

aₙ = a + (n - 1)d

a = - 3 + (11 - 1) (5 / 2)

= - 3 + 10 × (5 / 2)

= - 3 + 25

a₁₁ = 22

The correct option is B - 22. Thus, the11^{th} term of the AP is 22.

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 5

**Video Solution:**

## Choose the correct choice in the following and justify: i) 30ᵗʰ term of the AP: 10, 7, 4,..., is a) 97 b) 77 c) - 77 d) - 87 ii) 11ᵗʰ term of the AP: -3, - 1/2, 2,..., is: a) 28 b) 22 c) - 38 d) - \(48{\Large\frac{1}{2}}\)

NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 2

**Summary:**

We have to choose the correct choice for the following i) 30^{th} term of the AP: 10, 7, 4,..., is a) 97 b) 77 c) - 77 d) - 87 ii) 11^{th} term of AP: -3, - 1/2, 2,..., is: a) 28 b) 22 c) - 38 d) - \(48{\Large\frac{1}{2}}\) :The 30th term of the AP 10,7,4.. and the 11th term of the AP -3, -1/2, 2.. are -77 and 22 respectively.

**☛ Related Questions:**

- In the following AP, find the missing terms in the boxes: i) 2, _, 26 ii) _, 13, _ , 3 iii) 5, _ , _ , 9 ½ iv) - 4, _ , _ , _ , _ , 6 v) _ , 38, _ , _ , _ , - 22.
- Which term of the AP: 3, 8, 13, 18……. is 78.
- Find the number of terms in each of the following APs: i) 7, 13, 19,..., 205 ii) 18, 15 ½, 13 ,..., - 47.
- Check Whether -150 is a term of the AP 11, 8, 5, 2 …..

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