Question

find the sum of the series 2+4+6+. +200

Answer 1

Hey

a = 2

d = 4 - 2 = 2

an = 200

an = a + (n - 1)d

200 = 2 + (n - 1)

198 = n - 1

n = 199

Sn = n/2 {a + an}

S199 = 199/2 {2 + 200}

= 199/2 x 202

= 20099

Answer 2

Heya!!

The given series is in A.P with common Difference between of 2

It's sum is given by

S200 = n/2 { a + an }

n is number of terms.

a is ist term

And an is anth term.

Here a = 2 an = 200

n =?

an = a + ( n - 1 ) d

200 = 2 + ( n -1 ) × 2

n = 100

So, number of terms is 100.

it's sum is = 100/2 ( 2 + 200 )

= 10100.