Question

Find the sum of all positive integers less than 100, which are not divisible by 3.

Answer please

Answer 1

Answer:

3267

Step-by-step explanation:

sum of integers not divisible by 3= sum of all integers - sum of integers                             divisible by 3

=(1+2+3+4+5+............................99) - (3+6+9+..................99)

=(99*100)/2 - (33/2)(3+99)       here,  n=33

=4950 - 1683

=3267

Answer 2

The required answer is 3267.

Step-by-step explanation:

Consider the provided information.

First find the sum of all positive integers less than 100.

1, 2, 3, 4,....99

Find the total number of terms by using the formula: $a_n=a+(n-1)d$

Substitute a=1, aₙ=99 and d=1 in above formula.

$99=1+(n-1)1\\98=n-1\\n=99$

To calculate the sum use the formula: $S_n=\frac{n}{2}[2a+(n-1)d]$

Substitute the respective values in the above formula.

$S_n=\frac{99}{2}[2(1)+(99-1)(1)]$

$S_n=\frac{99}{2}[2+98]\\S_n=50\times99\\s_n=4950$

Now the number divisible by 3 are 3,6,9,...99

Find the number of terms.

$a_n=a+(n-1)d\\99=3+(n-1)3\\\frac{96}{3}=n-1\\n=33$

Now calculate the sum.

$S_n=\frac{33}{2}[2(3)+(33-1)(3)]\\S_n=\frac{33}{2}[6+96]\\S_n=51 \times33\\S_n=1683$

Now subtract the sum of all positive integers less than 100 and divisible by 3 with sum of all positive integers less than 100.

4950-1683=3267

Hence, the required answer is 3267.

#Learn more

brainly.in/question/14273968

Find the sum of all even number between 1to150​