Question

find the sum of first 20 even natural numbers​

Answer 1

Answer:

• The first even number is 2. It follows now that the the nth term of first 20 number is 2n where n = 1,2,3…….20. Thus, the series is 2, 4, 6 , …40.
• This series could be visualize as a A.P. Series with first term a =2 and d = 2 and n = 20
• The formula for sum is S = n/2(2a +(n-1)d)
• = 20/2(2*2 + (20–1)*2) = 10(4+19*2)
• = 10(4 + 38) = 10*42 =420

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Answer 2

We have to find the sum n terms of the AP 2,4,6,...

Here a=2,d=4−2=2.

Therefore, Required sum Sn=2n[2a+(n−1)d]=2n[2×2+(n−1)×2]

⇒Sn=n[2+n−1]

⇒Sn=n(n+1)                        ...(1)

Put n=20 in (1), we get

S20=20(20+1)=420