Chapter 5 Arithmetic Progressions Ex 5.1

**Question 1.**

**Solution:**

(i) Given:

a_{1} = ₹ 15

a_{2} = ₹ 15 + ₹ 8 = ₹ 23

a_{3} = ₹ 23 + ₹ 8 = ₹ 31

List of fares is ₹ 15, ₹ 23, ₹ 31

and a_{2} – a_{1} = ₹ 23 – ₹ 15 = ₹ 8

a_{3} – a_{2} = ₹ 31 – ₹ 23 = ₹ 8

Here, a_{2} – a_{1} = a_{3} – a_{2}

Thus, the list of fares forms an AP.

**Question 2.**

Write first four terms of the AP, when the first term a and the common difference d are given as follows:

(i) a = 10, d = 10

(n) a = -2, d = 0

(iii) a = 4, d = -3

(iv) a = -1, d = 12

(v) a = -1.25, d = -0.25
**Solution:**

(i) Given: a = 10, d = 10

a_{1} = 10,

a_{2} = 10 + 10 = 20

a_{3} = 20 + 10 = 30

a_{4} = 30 + 10 = 40

Thus, the first four terms of the AP are 10, 20, 30, 40.

(ii) Given: a = – 2, d = 0

The first four terms of the AP are -2, -2, -2, -2.

(iii) a_{1} = 4, d = -3

a_{2} = a_{1} + d = 4 – 3 = 1

a_{3} = a_{2} + d = 1 – 3 = -2

a_{4} = a_{3} + d = -2 – 3 = -5

Thus, the first four terms of the AP are 4, 1, -2, -5.

(iv)

(v) a_{1} = -1.25, d = -0.25

a_{2} = a_{1} + d = -1.25 – 0.25 = -1.50

a_{3} = a_{2} + d = -1.50 – 0.25 = -1.75

a_{4} = a_{3} + d = -1.75 – 0.25 = -2

Thus, the first four terms of the AP are -1.25, -1.50, -1.75, -2.

**Question 3.**

For the following APs, write the first term and the common difference:

**Solution:**

**Question 4.**

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.

**Solution:**

(i) 2, 4, 8, 16, ……

a_{2} – a_{1} = 4 – 2 = 2

a_{3} – a_{2} = 8 – 4 = 4

a_{2} – a_{1} ≠ a_{3} – a_{2}

Thus, the given sequence is not an AP.