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Sum of N Terms of an AP

What is the s...

Question

What is the sum of the arithmetic series $1 + 3 + 5 + 7 + 9 + . . . + 99 ?$

A

1500

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B

2500

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C

3500

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D

4500

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Solution

The correct option is B $2500$
$a_{n} = a + (n - 1) d$
$\Rightarrow 99 = 1 + (n - 1) 2$
$\Rightarrow 99 - 1 = 2 n - 2$
$\Rightarrow 98 + 2 = 2 n$
$\Rightarrow 100 = 2 n$
$\Rightarrow n = 50$
$S_{n} = \frac{n}{2} [a_{1} + a_{n}]$
$\Rightarrow S_{n} = \frac{50}{2} [1 + 99]$
$\Rightarrow S_{n} = 25 [100]$
$\Rightarrow S_{n} = 2500$

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