find the sum of all natural numbers upto 200
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We have to find sum 4+8+12+...+200
Clearly, it is arithmetic progression.
Here, a=4,d=4
Let there are n terms and 200 is nth term. Then,
a+(n−1)d=200
⇒4+(n−1)4=200
⇒(n−1)4=196
⇒(n−1)=49
⇒n=50
Therefore,
S
50
=
2
50
[4+200]
⇒S
50
=25×204=5100
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