3. Find the sum of first 100 even natural
numbers.
(3 marks)
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The sum of the first 100 even natural numbers is 10100
Step-by-step explanation:
2,4,6,...,2n are the even natural numbers.
Here,
a1 = t1 = 2 , t2 = 4 , t3 = 6 , ...
d = t2 - t1
d = 4 - 2
d = 2
n = 100
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Formula to find the sum of first 100 even natural
Sn = n/2 [ 2a + (n-1) d]
S100 = 100/2 [ 2× 2 + (100-1) × 2]
= 100/2 [ 4 + 99 × 2]
= 100/2 ( 4 + 198 )
= 100/2 × 202
= 50 × 202
S100 = 10100
S100 = 10100
The sum of the first 100 even natural numbers is 10100
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