Answer :

Given:

First term, a = 1

Common Difference, d = 3 – 1 = 2

nth term, a _{ n } = 199

We know that nth term of an A.P is given by

a _{ n } = a + (n – 1)d

⇒ 199 = 1 + (n – 1)2

⇒ 199 – 1 = 2 n – 2

⇒ 199 – 1 + 2 = 2 n

⇒ 2 n = 200

Now sum of n terms of AP,

where, n = number of terms, a = first term, d = common difference and S_{n} is the sum up to n terms

⇒ S _{ n } = 50 [2 + 99 × 2]

⇒ S _{ n } = 50 [2 + 198]

⇒ S _{ n } = 50 × 200

⇒ S _{ n } = 10000

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