Question

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

विकल्प

• 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  ...[∵ 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

⇒ 798 = 21n

∴ n = `798/21` = 38