Asked by Han

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?

Answers

Answered by MathMate
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
Answered by Han
Thanks for your help :D
Answered by Han
by the way did you multiply the equation by 10 to get rid of the decimal to get a whole number?
Answered by MathMate
Yes, it makes life a little easier.
I love integers! :)
Answered by Han
alright thanks :D
Answered by Han
I have one last question. How did you know a=1?
Answered by Han
like sorry for the sequence 1, 4, 16 how did you get 1?
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