# 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

**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.

**☛ Related Questions:**

- In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?(i) The taxi fare after each km when the fare is ₹ 15 for the first km and ₹ 8 for each additional km.(ii) The amount of air present in a cylinder when a vacuum pump removes 1/4 of the air remaining in the cylinder at a time..
- Write first four terms of AP, When the first term a and the common difference d are given as follows:i) a = 10, d = 10ii) a = - 2, d = 0iii) a = 4, d = - 3iv) a = - 1, d = 1/2v) a = - 1.25, d = - 0.25
- Which of the following are APs? If they form an AP, Find the common difference d and write three more terms.i) 2, 4, 8, 16...ii) 2, 5/2 ,3, 7/2 ....iii) - 1.2, - 3.2, - 5.2, - 7.2....iv) - 10, - 6, - 2, 2......v) 3, 3 + √2,-3 + 2√2, 3 + 3√2....

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