Question

A geometric series has a first term of 1000, seven terms and a sum of 671 . find the common ratio.

Answer 1

sum = a(1-r^n)/(1-r), where a is the first term amd r is the common ratio.5375/8 =1000(1-r^7) /(1-r)5375/8000 = (1-r^7)/(1-r)5375(1-r) = 8000(1-r^7)5275 - 5375r = 8000 -8000r^7rearranging,-2725 = 5375r-8000r^7There are three solutions; see the link.--------------------------------------...Principal amount 750Interest rate 9 percent per year = 0.09Number of times compounded per year 4Number of years 12Amount after 12 years = 750 ( 1 +0.09 / 4)^(48)= 750(1.0225)^(48)Amount after 12 years = $2,182.23