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Question
In an AP if a = 1, an = 20 and Sn = 399, then n is ______.
Options
19
21
38
42
Solution
In an AP if a = 1, an = 20 and Sn = 399, then n is 38.
Explanation:
∵ Sn = `n/2[2a + (n - 1)d]`
339 = `n/2[2 xx 1 + (n - 1)d]`
798 = 2n + n(n – 1)d ...(i)
And an = 20
⇒ a + (n – 1)d = 20 ...[∵ an = 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
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