Chapter 5 Arithmetic Progressions Ex 5.1

Question 1.

Solution:
(i) Given:
a1 = ₹ 15
a2 = ₹ 15 + ₹ 8 = ₹ 23
a3 = ₹ 23 + ₹ 8 = ₹ 31
List of fares is ₹ 15, ₹ 23, ₹ 31
and a2 – a1 = ₹ 23 – ₹ 15 = ₹ 8
a3 – a2 = ₹ 31 – ₹ 23 = ₹ 8
Here, a2 – a1 = a3 – a2
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
a1 = 10,
a2 = 10 + 10 = 20
a3 = 20 + 10 = 30
a4 = 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) a1 = 4, d = -3
a2 = a1 + d = 4 – 3 = 1
a3 = a2 + d = 1 – 3 = -2
a4 = a3 + d = -2 – 3 = -5
Thus, the first four terms of the AP are 4, 1, -2, -5.

(iv)

(v) a1 = -1.25, d = -0.25
a2 = a1 + d = -1.25 – 0.25 = -1.50
a3 = a2 + d = -1.50 – 0.25 = -1.75
a4 = a3 + 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, ……
a2 – a1 = 4 – 2 = 2
a3 – a2 = 8 – 4 = 4
a2 – a1 ≠ a3 – a2
Thus, the given sequence is not an AP.