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What is the sum of first $20$ multiples of $13$ ?

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2720

2730

2740

2750

answer is B.

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Detailed Solution

The given multiples of

13

are,

13, 26, 39, . . . . .

The numbers form an AP with first term 13 and common difference 13.
So, we get

a = 13, d = 13, n = 20

We know that sum of first n terms of an AP,

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

On substituting the values, we get

\Rightarrow S_{20} = \frac{20}{2} [2 \times 13 + (20 - 1) 13]

\Rightarrow S_{20} = 10 [26 + 19 \times 13]

\Rightarrow S_{20} = 10 [26 + 247]

{\Rightarrow S}_{20} = 2730

Therefore, the sum of first 20 multiples of 13 is 2730.
Hence, the correct option is 2.

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