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Question

Find the sum of all natural numbers between 200 and 300 which are exactly divisible by 6.

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Solution

The arithmetic series is, 204 + 210 + 216 + ...... + 294
a=204,d=210204=6,Tn=294,Sn=?
To find Sn, we should first find the value of 'n'
Tn=294
a+(n1)d=294
204+(n1)6=294
204+6n6=294
198+6n=294
6n=294198=96
n=16
Sn=n2[a+Tn]
S16=162[204+294]=162×498=3984

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