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What is the sum of first $15$ terms of $2, 5, 8 . . .$ ?

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44

42

345

386

answer is C.

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Detailed Solution

The given sequence is

2, 5, 8 . .

.
So, we get
First term a = 2
Common difference,

d = 5 - 2

\Rightarrow d = 3

d = 8 - 5

\Rightarrow d = 3

We know that sum of first n terms of an AP is given as,

S_{n} = \frac{n}{2} \times [2 a + (n - 1) d]

.
Substituting

n = 15, a = 2, d = 5 - 2 = 3,

we get

S_{15} = \frac{15}{2} \times [2 \times 2 + (15 - 1) 3]

{\Rightarrow S}_{15} = \frac{15}{2} \times [2 \times 2 + 14 \times 3]

{\Rightarrow S}_{15} = \frac{15}{2} \times 2 [2 + 7 \times 3]

\Rightarrow S_{15} = 15 \times [2 + 21]

{\Rightarrow S}_{15} = 15 \times 23

{\Rightarrow S}_{15} = 345

Therefore, the sum of the first 15 terms of the AP is 345.
Hence, the correct option is 3.

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