Question

Find the sum of all natural numbers
less than 100 which are not multiples of 3​

Answer 1

Hey!!!Here is your solution

Answer:3267

Step-by-step explanation:

The numbers are

3,6,9,.....,96,99

which is an A.P with first term a_1=3, d=3 , a_n=99 ,where a_n is nth term of the A.P. ,d is common difference of A.P.

But we know

a_n=a_1+(n-1)d

99=3+(n-1)3

n=33

Thus sum of n terms of an AP is S_n=(n/2)(2a_1+(n-1)d)

S_33=(33/2)(2xx3+(33-1)xx3)

=(33/2)(102)=1683

Sum of n natural numbers is=(n(n+1))/2

Thus sum of first 99 ,natural number is

S=(99xx(99+1))/2 =4950

Sum of numbers non divisible by 3 and less than 100=S-S_33

=3267

Hope it helps you..

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