Sum of first $15$ terms of $2 + 5 + 8 + . . .$ is?

44

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42

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345

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386

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Solution

The correct option is B $345$
Difference between terms $= 5 - 2 = 8 - 5 = 3$
We can observe that difference between two consecutive terms is equal, hence the terms are in A.P.
Sum of fist n terms in an A.P. is given by the formula: $S_{n} = \frac{n}{2} \times [2 a + (n - 1) d]$
Given $n = 15, a = 2, d = 5 - 2 = 3,$
$S_{n} = \frac{15}{2} \times [2 \times 2 + (15 - 1) 3]$
$S_{n} = \frac{15}{2} \times 46$
$S_{n} = 345$

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