Find the sum of the terms of the finite AP :
1, 3, 5, 7,…,199

10000

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12000

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13333

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20000

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Solution

The correct option is A 10000
Given, $a = 1, d = 2$
$a_{n} = l = 199$
$a + (n - 1) d = 199$
$1 + (n - 1) 2 = 199$
$\Rightarrow 1 + 2 n - 2 = 199$
$\Rightarrow 2 n = 200$
$n = 100$
Sum of n terms: $S_{n} = \frac{n}{2} (a + l)$
So, sum of the terms of the given $A P = S_{100} = \frac{100}{2} (1 + 199)$
$= 10000$

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