Question

In an A.P., ten times of its tenth term is equal to thirty times of its 30^th term. Find its 40^th term.

Answer 1

The general term of an A.P. is given by

t_n = a + (n – 1)d

Given,

10 × t₁₀ = 30 × t₃₀

`=>` 10 × (a + 9d) = 30 × (a + 29d)

`=>` a + 9d = 3a + 87d

`=>` 2a + 78d = 0

`=>` a + 39d = 0

`=>` a = –39d

Now, t₄₀ = a + 39d

= –39d + 39d

= 0