Question

In an A.P. a₁, a₂, a₃,...,a_n,...., if a₁ = 1, a_n = 20 and S_n = 399, then the value of n is ______.

Answer 1

In an A.P. a₁, a₂, a₃,...,a_n,...., if a₁ = 1, a_n = 20 and S_n = 399, then the value of n is 38.

Explanation:

Use the sum formula `S_n = n/2 (a_1 + a_n)`.

So `399 = n/2 (1 + 20)`

= `(21n)/2`

Hence 21n = 798 and n = `798/21` = 38.