Chapter 11.2, Problem 30WE

To determine

To calculate:

The divisible number by $7$ between $50$ and $500$

Answer to Problem 30WE

There are $62$ numbers which are divisible by $7$ between $50$ and $500$

Explanation of Solution

Given information:

Number between $50$ and $500$

Calculation:

The first number between $50$ and $500$ is $56$ and the last number is $497$ which are divisible by $7$

Now, first term is $a_1=56$ and the last term is $a_n=497$ . The common ratio between each term is $7$ .

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

  $\begin{array}{l}{a}_n=a_1+\left(n-1\right)d\\ 497=56+\left(n-1\right)7\\ 441=7n-7\\ 7n=434\\ n=62\end{array}$