SOLUTION: A geometric sequence has a term of a4= �54 and a common ratio of r = 3. What is the rule for the nth term?

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Question 862286: A geometric sequence has a term of a4= �54 and a common ratio of r = 3. What is the rule for the nth term?
Found 2 solutions by ewatrrr, Theo:
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
A4 = -54
r = 3
The formula is:
An = A1 * r^(n-3)
Since you have A4 and r, you can solve for A1.
the formula is:
A4 = A1 * r^(4-1)
replace variable with their known values and you get:
-54 = A1 * 3^(3)
simplify this to get:
-54 = A1 * 27
divide both sides of this equation by 27 to get:
-54/27 = A1 which makes A1 = -2.
Now that you have A1, you can apply the formula to get the nth term.
The formula is An = A1 * r^(n-1)
replace A1 with -2 and r with 3 to get:
An = -2 * 3^(n-1)
If n is equal to 4, then this formula will get you:
A4 = -2 * 3^(3) which will get you A4 = -2 * 27 which will get you A4 = -54.
we're back where we started, which is good because the formula works for n = 4 and will also work for n = any other number.