Find the sum to $n$ terms of A.P whose $k t h$ term is $5 k + 1$ .

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Solution

Common difference
$= 5 (k + 1) + 1 - (5 k + 1)$
$= 5 k + 5 + 1 - 5 k - 1$
$= 5$
first term $= 6$ so sum $= \frac{n}{2} (12 + (n - 1) \times 5)$
$= \frac{n}{2} (5 n + 7) = \frac{n (5 n + 7)}{2}$

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