Chapter 11.5, Problem 28WE

To determine

To calculate:

Sum of the positive two-integers that are not divisible by $5$ .

Answer to Problem 28WE

Sum of the positive two-integers that are not divisible by $3$ is $3960$ .

Explanation of Solution

Give information:

The positive two-integers that are not divisible by $3$ ..

Calculation:

Given is The positive two-integers that are not divisible by $3$ ,

The sum of positive two-integers that are not divisible by $3$ , find the sum of all positive two-digit integers.

The first sum is $10+15+\mathrm{...}+90+95$

Using the formula for the sum of an arithmetic series,

  $=\frac{n\left(t_1+t_n\right)}{2}$

This is an arithmetic series with $t_1=10,t_n=95,n=\left(95-10\right)/5+1=18$

Sum is,

  $\begin{array}{l}\frac{18\left(10+95\right)}{2}\\ =9.105\\ =945\end{array}$

The sum of two digits integers is $10+11+\mathrm{...}+99=90\left(10+99\right)/2=4905$

To get final answer, subtract

  $\begin{array}{l}4905-945\\ =3960\end{array}$

Therefore, Sum of the positive two-integers that are not divisible by $3$ is $3960$ .