Question

A computer virus initially Infects one fle, then the total number of files Infected triples every minute. a) What are the first three terms of this sequence? b) Write an equation to represent this sequence. c) How many files will be infected after 15 minutes?

Answer 1

The computer virus initially infects one file, then for every minute the number files gets tripled. So the first term will be 1, the second will be 3, the third will be 9 and so on. The sequence is:

`\mleft\lbrace1,3,9,\ldots\mright\rbrace`

This is a geometric sequence, where each term is related to its previous by the product of a constant number. For these cases we can represent the sequence as shown below:

`\begin{gathered} a_n=a_1\cdot r^(n-1) \\ a_n=1\cdot3^(n-1) \\ a_n=3^(n-1) \end{gathered}`

To find how many files will be infected after 15 minutes we need to make n=15 and solve for a, we have:

`\begin{gathered} a_(15)=3^(15-1)=3^(14) \\ a_(15)=4782969 \end{gathered}`