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Question
Find the sum of n terms of the A.P. whose kth terms is 5k + 1.
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Solution
\[\text { Given }: \]
\[ a_k = 5k + 1\]
\[\text { For} k = 1, a_1 = 5 \times 1 + 1 = 6\]
\[\text { For }k = 2, a_2 = 5 \times 2 + 1 = 11\]
\[\text { For } k = n, a_n = 5n + 1\]
\[ \therefore S_n = \frac{n}{2}\left[ a + a_n \right]\]
\[ \Rightarrow S_n = \frac{n}{2}\left[ 6 + 5n + 1 \right] = \frac{n}{2}\left( 5n + 7 \right)\]
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