Question

If sum of the 3^rd and the 8^th terms of an AP is 7 and the sum of the 7^th and the 14^th terms is –3, find the 10^th term.

Answer 1

Let the first term and common difference of an AP are a and d, respectively.

a₃ + a₈ = 7 and a₁₇ + a₁₄ = -3

⇒ a + (3 – 1)d + a + (8 – 1)d = 7   .......[∵ a_n = a + (n- 1 )d]

and a + (7 – 1 )d + a + (14 – 1 )d = – 3

⇒ a + 2d + a + 7d = 7

And a + 6d + a + 13d = -3

⇒ 2A + 9d = 7  .......(i)

And 2a + 19d = – 3 ......(ii)

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

10d = – 10

⇒ d = – 1

2a + 9(-1) = 7   ......[From equation (i)]

⇒ 2a – 9 = 7

⇒ 2a = 16

⇒ a = 8

∴ a₁₀ = a + (10 – 1)d

= 8 + 9(–1)

= 8 – 9

= –1