A geometric series has three terms. The sum of the three terms is 42. The third term is 3.2 times the sum of the other two. What are the terms?

Answer 1

Let the series be
a, ax, ax²

"The third term is 3.2 times the sum of the other two"
means
ax²/(a+ax)=3.2
cross multiply:
ax²=3.2(a+ax)
cancel common factor a (≠0) & multiply by 10
10x²-32x-32=0
=>x=4 or x= -4/5
Reject solution where |x|<1
x=4, or
"The sum of the three terms is 42" means
a(1+4+16)=42
a=2

So the terms are 2, 8, 32

Answer 2

Thanks for your help :D

Answer 3

by the way did you multiply the equation by 10 to get rid of the decimal to get a whole number?

Answer 4

Yes, it makes life a little easier.
I love integers! :)

Answer 5

alright thanks :D

Answer 6

I have one last question. How did you know a=1?

Answer 7

like sorry for the sequence 1, 4, 16 how did you get 1?