Question

Find the sum :2+4+6+8+......+200

Answer 1

1500 is your answer of this question

Answer 2

Answer:

heya mate there's your answer

given series 2+4+6+8+..........+200 is in AP.

let the first term of the AP be a1=2

second term be a2=4

and common difference be d.

d=a2-a1

d=4-2

d=2

so common difference is d=2

we know that,

nth term of AP is,

an=a1+(n-1)d

let 200 be the nth term of the AP.

200=2+(n-1)(2)

200-2=(n-1)(2)

198=(n-1)(2)

n-1=198/2

n-1=99

n=99+1

n=100

so 200 is the 100th term in the AP.

Sum of n terms in an AP is

Sn=n/2[2a1+(n-1)d]

so sum of 100 terms is,

S100=100/2[2×2+(100-1)(2)]

=100×2/2 [2+(100-1)]

=100[2+99]

=100(101)

=10100

so, 2+4+6+8+ ........+200=10100

OR

sum of n even natural numbers is = n (n+1)

there are 100 even numbers from 2 to 200

so, =100(100+1)

=100(101)

=10100

hope it helps you..........

Thank you!!!