Chapter 11.2, Problem 29WE

To determine

To calculate:

The number of multiplies of $3$ between $100$ and $1000$

Answer to Problem 29WE

There are $298$ numbers of multiplies of $3$ between $100$ and $1000$ .

Explanation of Solution

Given information:

Number between $100$ and $1000$

Calculation:

The first number between $100$ and $1000$ is $105$ and the last number is $999$ which is multiply of $3$

Now, first term is $a_1=108$ and the last term is $a_n=999$ . The common ratio between each term is $3$ .

Now, the number of the terms in the given sequence is calculated as:

  $\begin{array}{l}{a}_n=a_1+\left(n-1\right)d\\ 999=108+\left(n-1\right)3\\ 891=3n-3\\ 3n=894\\ n=298\end{array}$