Question

You start a chain email and send it to 3 friends. The process continues and each of your friends forward the email to 3 other people. What is an expression for the nth term an?

Answer 1

`a_(n)=3^(n)`

Explanation:

We can start solving this problem by making a list of the number of chain emails that are sent on each round:

Round one:

`a_(1)=3`

which represents the three friends you send the mail to.

Round two:

`a_(2)=3*3=9`

since each of your friends sends the mail to another three friends, then we multiply the original 3 friends by 3 to get a total of 9.

Round three:

`a_(3)=3*3*3=9*3=27`

on the next round we multiply the previous 9 persons by 3 mails each giving us a total of 27 persons receiving the mail. A patter starts showing here. Notice that for each round we need to take the previous round number an multiply it by 3. When we have a number being multiplied by itself n times, we rewrite it as a power, so the expression for the nth term will be:

`a_(n)=3^(n)`

which is our final answer.