In a similar outbreak the disease spread to infect fewer peo

In a similar outbreak, the disease spread to infect fewer people over time. The total number of people infected was modeled by the following geometric series. 150+120+96+384/5+1536/25+... what is the total number of people infected in the outbreak?

Solution

The total number of people infected was modeled by the following geometric series. 150+120+96+384/5+1536/25+...

commonration : r

r = 120/150 =4/5

= 96/120 =8/10 = 4/5

= 384/5*96 = 4/5

So, r = 4/5

first term a1 = 150

Geomtric series sum = a1/( 1 -r) = 150/( 1-r) = 150/( 1- 4/5)

= 150/(1/5) = 150 *5 = 750

total number of people infected in the outbreak = 750