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

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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 $\Rightarrow$ a + (n – 1)d = 20 ...[∵ an = a + (n – 1)d] $\Rightarrow$ 1 + (n – 1)d = 20 $\Rightarrow$ (n – 1)d = 19 ...(ii) Using equation (ii) in equation (i), we get 798 = 2n + 19n $\Rightarrow$ 798 = 21n $\therefore$ n = $\frac{798}{21}$ = 38

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