Choose the correct alternative answer for the following question . In an A.P. 1st term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....

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It is given that, First term (a) = 1 Last term (tn) = 20 Sum of terms (Sn) = 399 We know that, t_n = a + \left( n - 1 \right)d S_n = n/2\left( 2a + \left( n - 1 \right)d \right) \Rightarrow S_n = n/2\left( a + \left( a + \left( n - 1 \right)d \right) \right) \Rightarrow S_n = n/2\left( a + t_n \right) \Rightarrow 399 = n/2\left( 1 + 20 \right) \Rightarrow 399 = 21n/2 \Rightarrow 21n = 399 $\times$ 2 \Rightarrow n = $\frac{798}{21}$ \Rightarrow n = 38

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