Evaluate: $2 + 7 + 12 + 17...$ to n terms.

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Solution

Here,the given series is $A . P$

as $7 - 2 = 12 - 7 = 17 - 12 = 5$

So,

$a = 2, d = 5$

$a_{n} = a + (n - 1) d$

$a_{n} = 2 + (n - 1) 5$

$a_{n} = 2 + 5 n - 5$

$a_{n} = 5 n - 3$

$S_{n} = \frac{n}{2} (a + l)$

$S_{n} = \frac{n}{2} (2 + 5 n - 3)$

$S_{n} = \frac{n}{2} (5 n - 1)$

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