In a geometric sequence, the sum of first four terms is 16 times the sum of the following four term, find the common ratio?
Sn =( a(1-r^n)) /1-r
anyone can tell me how to start or resolve this ??
Looks to me to imply:
. I suspect that this will give you a lot of terms cancelling out, leaving you with a deceptively simple exponential equation to finish (hint: let ). I don't know if there's a better approach.
If the sum of the first four terms is larger than the sum of the next four then . This will come in useful for checking the answer.
Now to put this expression back into the original expression:
Do some cancelling and your equation will become clear. Since you have an even power of r there are two possible answers
In a geometric sequence, the sum of first four terms
is 16 times the sum of the following four term.
Find the common ratio.
We are given that:.
We have two equations to solve: