Question

Find the sum of all natural numbers not exceeding 1000 which are divisible by 4 but not divisible by 8

Answer 1

Lets start.

The following sequence forms an A.P.

51,52,53,…….,100

Here,

First term (a)=51

Common difference (d)=1

Last term (tn)=100

To solve further we need two formulae i.e.

tn=a+(n-1)d

Sn=n/2[2a+(n-1)d]

Now using first formula and substituting the values we get,

100=51+(n-1)1

100=51+n-1

100=50+n

n=100–50

n=50

We get n=50.

Now using second formula substituting the values we get,

S50=50/2[2×51+(50–1)1]

S50=25[102+49]

S50=25×151

S50= 3775

So the sum of all natural number from 51 to 100 is 3775.