Chapter 11.3, Problem 1CYP

To determine

Find the number of people will receive the E − mail on the ninth round of forwarding.

Answer to Problem 1CYP

262,144 people

Explanation of Solution

Given:

Shira receives a joke in an E − mail that asks her to forward it to four of her friends. She forwards it, and then each of her friends forwards it to four of their friends, and so on. If the pattern continues, how many people will receive the E − mail on the ninth round of forwarding?

Concept Used:

Shira receives a joke in an E − mail that asks her to forward it to four of her friends.

So the first term $a_1=4$

She forwards it, and then each of her friends forwards it to four of their friends, and so on.

This means the common ratio: $r=4$

Find the number of people will receive the E − mail on the ninth round of forwarding. This represents the number of terms is 9

Calculation:

  $a_1=4;r=4;n=9;\text{find}{a}_9$

  $\begin{array}{l}{a}_n=a_1·r^{n-1}\\ a_9=a_1·r^{9-1}=a_1·r^8=4·4^8=4^9=262,144\end{array}$

Thus, 262,144 people will receive the E − mail on the ninth round of forwarding