Question

The sum of first 14 terms of an A.P. is 1050 and its 14^th term is 140. Find the 20^th term.

Answer 1

Let 'a' be the first term and 'd' be the common difference of the given A.P.

Given,

S₁₄ = 1050

`\implies 14/2 [2a + (14 - 1)d] = 1050`

`\implies` 7[2a + 13d] = 1050

`\implies` 2a + 13d = 150 

`\implies` a + 6.5d = 75   ...(i)

And t₁₄ = 140

`\implies` a + 13d = 140   ...(ii)

Subtracting (i) from (ii), we get

6.5d = 65

⇒ d = 10

⇒ a + 13(10) = 140

⇒ a = 10

Thus, 20^th term = t₂₀ 

= 10 + 19d

= 10 + 19(10)

= 200