SOLUTION: Here is my problem: There are two geometric sequences with 3rd term 5 and 5th term 80. What are the two possible values of the 4th term?
I have my two equations of
5=ar^2
80=
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-> SOLUTION: Here is my problem: There are two geometric sequences with 3rd term 5 and 5th term 80. What are the two possible values of the 4th term?
I have my two equations of
5=ar^2
80=
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Question 1062748: Here is my problem: There are two geometric sequences with 3rd term 5 and 5th term 80. What are the two possible values of the 4th term?
I have my two equations of
5=ar^2
80=ar^4
(a is first term and r is mutliplier quantity)
I then go to 80/5 = r^4/r^2 which then ends up being 16r = r^2 and over to r^2 - 16r = 0. Completing the square gives me r^2 - 16r + 64 = 64. Problem is that then gets me right back to my pre-completing the square part. My other option is to do r(r-16) = 0 which gives me r = 0 and 16 which can't work because r = 0 doesn't give me any workable answer. So I must assume I'm doing something wrong.
Thanks for any help! Answer by jim_thompson5910(35256) (Show Source):
Solving for r leads to or . This is after you apply the square root to both sides. Don't forget to use the plus/minus.
Now that we know that or , we can use this to find the fourth term
fourth term = r*(third term)
fourth term = r*5
If r = 4, then
fourth term = r*5
fourth term = 4*5
fourth term = 20
OR
If r = -4, then
fourth term = r*5
fourth term = -4*5
fourth term = -20
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Question: There are two geometric sequences with 3rd term 5 and 5th term 80. What are the two possible values of the 4th term?
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