MATH SOLVE

2 months ago

Q:
# What is the common ratio for the geometric sequence? −15,−9,−275,−8125,... The initial value of the boat is $11,200. The value of the boat after t years is $11,200. The value of the boat decreases by $11,200 each year. The value of the boat increases by $11,200 each year.

Accepted Solution

A:

Answer: Common ratio is [tex]\frac{3}{5}.[/tex]

Step-by-step explanation: Given sequence −15,−9,−275,−8125,...The general terms of a geometric sequence are: [tex]a, ar, ar^2, ar^3, ar^4 ......[/tex].In common ratio is given by dividing next term from previous term [tex]\frac{ar}{a} = r[/tex]Therefore, in order to find the common ratio for the given geometric sequence, we need to divide second term by first term or third term by second term.Dividing second term by first term, we get [tex]\frac{-9}{-15}[/tex]Dividing top and bottom by -3, we get [tex]\frac{3}{5}[/tex].Therefore, common ratio is [tex]\frac{3}{5}.[/tex]

Step-by-step explanation: Given sequence −15,−9,−275,−8125,...The general terms of a geometric sequence are: [tex]a, ar, ar^2, ar^3, ar^4 ......[/tex].In common ratio is given by dividing next term from previous term [tex]\frac{ar}{a} = r[/tex]Therefore, in order to find the common ratio for the given geometric sequence, we need to divide second term by first term or third term by second term.Dividing second term by first term, we get [tex]\frac{-9}{-15}[/tex]Dividing top and bottom by -3, we get [tex]\frac{3}{5}[/tex].Therefore, common ratio is [tex]\frac{3}{5}.[/tex]