is the sum of the following AP 1, 3, 5, 7 …199.

10000

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12000

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20000

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Solution

The correct option is A 10000
$G i v e n, a = 1, d = 2, a_{n} = l = 199 a + (n - 1) d = 199$
$1 + (n - 1) 2 = 199$
$\Rightarrow 1 + 2 n - 2 = 199$
$\Rightarrow 2 n = 200$
$n = 100$
$S_{n} = \frac{n}{2} (a + l)$
$S_{n} = \frac{100}{2} (1 + 199)$
$S_{n} = 10000$

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