Question

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

Answer 1

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

According to the questiuon,

a₃ + a₈ = 7 and a₇ + 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