Learn It Part 2

Let’s take a closer look at arithmetic sequences and geometric sequences. Suppose strands of a new, unknown virus have entered the United States. The Centers for Disease Control and Prevention (CDC) are monitoring the growth of the virus. The CDC determines that one strand of the virus, identified as Strand A, grows arithmetically with a common difference of 11. The CDC determines the other strand, identified as Strand B, grows geometrically with a common ratio of 1.11.

Complete the pattern below, showing the number of people who contract the strands of the virus. You may print a copy of the tables Opens a new window, or copy each table onto a separate sheet of paper to complete this activity. Round any decimals to the thousandths place. When you are done, click the Show Answer button to check your work.

Strand A

A table with eight columns and two rows. The top row is labeled “Day” and increases from 0 to seven in increments of one. The bottom row is labeled “Number of infected people” and the eight columns are left blank to fill in. Seven blanks appear below the bottom row for the common difference to be filled in.

Strand B

A table with eight columns and two rows. The top row is labeled “Day” and increases from 0 to seven in increments of one. The bottom row is labeled “Number of infected people” and the eight columns are left blank to fill in. Seven blanks appear below the bottom row for the common ratio to be filled in.

Tip

Strand B grows by 11%. The common ratio is 1.11 because it takes into account the number of people previously infected by the virus.

The Strand A virus follows an arithmetic sequence because it follows an additive pattern. The common difference is 11. Choose a term in the pattern and subtract the previous term, and you will get this common difference.

Did you recognize the Strand B virus? This is the Ebola virus that entered the United States in 2014.

The Ebola virus is an example of a geometric sequence because it follows a multiplicative pattern. The common ratio is 1.11. Choose a term in the pattern and divide the previous term, and you will get this common ratio.

The Ebola virus has many scientists worried because it spreads very quickly. It may not appear to be too threatening in the tables you just completed, but if you extend the tables past sixty days, the growth of the Ebola virus greatly overtakes the growth of Strand A.

Strand A

A table with eight columns and two rows. The top row is labeled “Day” and increases from 0 to seven in increments of one. The bottom row is labeled “Number of infected people” and the eight columns are one, twelve, twenty-three, thirty-four, forty-five, fifty-six, sixty-seven, and seventy-eight. A ripped off column has been attached to the table, with the top row entry of sixty-five and the bottom row entry of seven hundred sixteen.

Strand B

A table with eight columns and two rows. The top row is labeled “Day” and increases from 0 to seven in increments of one. The bottom row is labeled “Number of infected people” and the eight columns are one, one and eleven hundredths, one and two hundred thirty-two thousandths, one and three hundred sixty-eight thousandths, one and five hundred eighteen thousandths, one and six hundred eighty-five thousandths, one and eight hundred seventy thousandths, and two and seventy-six thousandths. A ripped off column has been attached to the table, with the top row entry of sixty-five and the bottom row entry of eight hundred eighty-three and sixty-seven thousandths.