For the following APs, write the first term and the common difference:
i) 3, 1, - 1, - 3,…
ii) - 5, - 1, 3, 7,…
iii) 1/3, 5/3, 9/3, 13/3,…
iv) 0.6, 1.7, 2.8, 3.9,…

Solution:

The general form of an arithmetic progression is a, (a + d), (a + 2d), (a + 3d),… where a is the first term and d is a common difference.

i) 3, 1, - 1, - 3,… are in AP

First term, a₁ = 3

Common difference, d = a₂ - a₁

d = 1 - 3 = - 2

Thus, the first term is 3 and the common difference is - 2.

ii) - 5, -1, 3, 7,… are in AP

First term, a₁ = - 5

Common difference, d = a₂ - a₁

d = - 1 - (- 5) = - 1 + 5 = 4

Thus, the first term is - 5 and the common difference is 4.

iii) 1/3, 5/3, 9/3, 13/3,… are in AP

First term, a₁ = 1/3

Common difference, d = (a₂ - a₁)

d = 5/3 - 1/3 = 4/3

Thus, the first term is 1/3 and the common difference is 4/3.

iv) 0.6, 1.7, 2.8, 3.9,… are in AP

First term, a₁ = 0.6

Common difference, d = a₂ - a₁

d = 1.7 - 0.6 = 1.1

Thus, the first term is 0.6 and the common difference is 1.1.

☛ Check: NCERT Solutions Class 10 Maths Chapter 5

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Video Solution:

For the following APs, write the first term and the common difference: i) 3, 1, - 1, - 3,… ii) - 5, - 1, 3, 7,… iii) 1/3, 5/3, 9/3, 13/3,… iv) 0.6, 1.7, 2.8, 3.9,… 

NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.1 Question 3

Summary:

For the following APs, the first term and the common difference are i) 3, 1, - 1, - 3,… ; a = 3, d = - 2 ii) - 5, - 1, 3, 7,…; a = -5, d = 4, iii) 1/3, 5/3, 9/3, 13/3,…; a = 1/3, d = 4/3 iv) 0.6, 1.7, 2.8, 3.9,…; a = 0.6, d = 1.1 respectively.

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