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

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Solution

$a_{k} = a + (k - 1) d = 5 k + 1$
$\Rightarrow a + k d - d = 5 k + 1$
By compairing, d=5 & a-d=1
a=1+d
a=1+5=6
$S_{n} = \frac{n}{2} [2 a + (n - 1) d]$
$S_{n} = \frac{n}{2} [12 + (n - 1) 5]$
$S_{n} = \frac{n}{2} [5 n + 7]$

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