Question

a geometric series has 3 terms. the sum of the three terms is 42. the third term is 3.2 times the sum of the other two terms. what are the three terms?

Answer 1

ok so the series is x,y,and z
x+y+z=42
3.2(x+y)=z

rearrange the first equation to get
z=42-x-y

3.2(x+y)=42-x-y
OR
3.2x+3.2y=42-x-y

combine the x's and y's to one side

4.2x+4.2y=42

divide everything by 4.2

x+y=10

place that into the first equation

10+z=42

subtract 10 from both sides

z=32

the other 2 terms have to be smaller by a constant multiple knowing the number 32 divides nicely by 8 and 4 we can try both of those number i started with 8 so 8times4 gives you 32 and if you divide 8 by 4 you get 2 8=y and x=2 x+y=10 those work!! hope this helps