Question

Match the APs given in column A with suitable common differences given in column B.

Column A	Column B
(A1) 2, –2, –6, –10,...	(B1) `2/3`
(A2) a = –18, n = 10, an = 0	(B2) –5
(A3) a = 0, a10 = 6	(B3) 4
(A4) a2 = 13, a4 = 3	(B4) –4
	(B5) 2
	(B6) `1/2`
	(B7) 5

Answer 1

Column A	Column B
(A1) 2, –2, –6, –10,...	(B4) –4
(A2) a = –18, n = 10, an = 0	(B5) 2
(A3) a = 0, a10 = 6	(B1) `2/3`
(A4) a2 = 13, a4 = 3	(B2) –5

Explanation:

(A₁): 2, –2, –6, –10,...

Here, common difference, d = –2 – 2 = –4

(A₂): a_n = a + (n – 1)d

⇒ 0 = –18 + (10 – 1)d

18 = 9d

∴ Common difference, d = 2

(A₃): a₁₀ = 6, a = 0

⇒ a + (10 – 1)d = 6   ...[∵ a_n = a + (n – 1)d]

⇒ 0 + 9d = 6   ...[∵ a = 0 (given)]

d = `6/9 = 2/3`

(A₄): a₂ = 13, a₄ = 3

⇒ a + (2 – 1)d = 13  ...[∵ a_n = a + (n – 1)d]

⇒ a + d = 13   ...(i)

And a₄ = 3

⇒ a + (4 – 1)d = 3

∴ a + 3d = 3  ...(ii)

On subtracting equation (i) from equation (ii), we get

2d = –10

⇒ d = 5