Question

Find the value of 2+ 4+ 6+ .... + 100th even number.?

Answer 1

Hope this helps........

Answer 2

Given,

A series 2+ 4+ 6+ ,... + 100th term

To find,

Find the value of given series.

Solution,

4-2 = 2, 6-4 = 2

The given series is in arithmetic progression with a common difference 2.

a = 2 which is the first term of the Arithmetic Progression

Now, the 100th term of the AP = a+99d

⇒  100th term of AP = 2 + 99(2)

⇒  2 + 198

⇒  200.

Sun of AP is calculated by = Sn = n/2(2a+(n-1)d)

⇒  S100 = (100/2) [(2(2)+(100-1)2]

⇒  S100 = 50[4+99(2)]

⇒  S100 = 50[4+198]

⇒  S100 = 50[202=]

⇒  S100 = 10100.

Hence, the the value of 2+ 4+ 6+ .... + 200 is 10100.