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Formula for Sum of n Terms of an AP

Find the sum ...

Question

Find the sum of the series : 3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 + .... to 3n terms.

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Solution

In the given series 3 + 5 + 7 + 9 + .... to 3n.
Here,
a = 3
d = 2
Number of terms = 3n
The sum of n term is
$S_{n} = \frac{n}{2} [2 a + (n - 1) d] \Rightarrow S_{3 n} = \frac{3 n}{2} [6 + (3 n - 1) 2] = 3 n (2 n + 3)$

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