Question

In an AP if a = 1, a_n = 20 and S_n = 399, then n is ______.

Options

• 19

• 21

• 38

• 42

Answer 1

In an AP if a = 1, a_n = 20 and S_n = 399, then n is 38.

Explanation:

∵ `S_n = n/2 [2a + (n - 1)d]`

339 = `n/2 [2 xx 1 + (n - 1)d]`

798 = `2n + n(n - 1)d`  ........(i)

And `a_n` = 20

⇒ `a + (n - 1)d` = 20  .....`[because a_n = a + (n - 1)d]`

⇒ `1 + (n - 1)d` = 20

⇒ `(n - 1)d` = 19  ......(ii)

Using equation (ii) in equation (i), we get

798 = `2n + 19n`

⇒ 978 = `2n`

∴ n = `798/21` = 38