Find the sum of the following AP 1, 3, 5, 7 …199. Options: A . &nbsp 10000 B . &nbsp 12000 C . &nbsp 13333 D . &nbsp 20000

Answer: Option A : A G i v e n , a = 1 , d = 2 , a n = l = 199 a + ( n − 1 ) d = 199 1 + ( n − 1 ) 2 = 199 ⇒ 1 + 2 n − 2 = 199 ⇒ 2 n = 200 n = 100 S n = n 2 ( a + l ) S n = 100 2 ( 1 + 199 ) S n = 10000

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

Question

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

Options:

A . 10000

B . 12000

C . 13333

D . 20000

Answer: Option A
:
A

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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