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What is the sum of first 24 terms of the arithmetic progression where, the common difference $d$ and the first term $a$ are given, $a = \sqrt{2}, d = \sqrt{2}$ ?

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300

\sqrt{2}

150

\sqrt{2}

250

\sqrt{2}

325

\sqrt{2}

answer is A.

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Detailed Solution

It is given that a =

\sqrt{2}

, d =

\sqrt{2}

and n = 24.
We know that sum of first n terms of an AP is given as,

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

.
Putting the values in the formula, we get

S_{24}

\frac{24}{2} \times [2 (\sqrt{2}) + (24 - 1) (\sqrt{2})]

{\Rightarrow S}_{24} = 12 \times (2 \sqrt{2} + 23 \sqrt{2})

\Rightarrow S_{24} = 12 \times (25 \sqrt{2})

{\Rightarrow S}_{24} = 300 \sqrt{2}

Therefore, the sum of first 24 terms of the AP is

300 \sqrt{2}

.
Hence, the correct option is 1.

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