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
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! :)
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?
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.