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Question

Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.

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Solution

All natural numbers bwetween 1 and 145 which are divisible by 4 are,
4,8,12,16,...........,144 forms an A.P
with a=4 and d=4

Let, tn=144

a+(n1)d=144

4+(n1)4=144

4(n1)=140

n1=35

n=36

Now, Sn=n2[a+l]

=362[4+144]

=18×148

=2664

Hence, The required sum =2,664

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