Question

Find the sum of all three digit numbers divisible by 4 and find their sum

Answer 1

Hi there!
Here's the answer:

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The smallest 3-digit No. is 100
The smallest 3-digit No. divisible by 4 is also 100.

The largest 3-digit No. is 999
The largest 3-digit No. divisible by 4 is 996

•°• The Required No.s are
100, 104, 108, 112, …………… 992, 994, 996.

The sum of these Numbers
= 100+104+108+112+……+994+996

The No.s are in A.P

a= 100
d = 4
l = 996

where
a- the first term
d - common difference
l - the last term

No. of terms in an A.P is given by
n = [( l - a) / d] + 1
=> n = [ (996 - 100)/4 ] + 1
=> n = (896/4) +1
=> n = 224 + 1
=> n = 225

Sum of terms in A.P
Sn = (n/2) [ a + l ]
= (225/2) [100 + 996]
= [ 225 × 1096] / 2
= 225 × 548
= 123300

•°• Required Sum = 123300

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Hope it helps