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