SOLUTION: 1. Find a formula for the nth term of the following sequence: 4, 12, 36, 108, 324, . . . . 2. Find the 8th of the geometric sequence whose third term is 1/25 and whose sixth is 1/

Question 1168777: 1. Find a formula for the nth term of the following sequence: 4, 12, 36, 108, 324, . . . .
2. Find the 8th of the geometric sequence whose third term is 1/25 and whose sixth is 1/3125
3. What are the first five terms of the geometric sequence whose first term is a1 = 2 and whose
common ratio is r = 3.
4. Find the 10th term of the geometric sequence whose first term is 8 and whose common ratio is ¼.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
1. This is a geometric sequence with common ratio, r = 36/12 = 12/4 = 3
The first term, a_1 = 4.
Thus the formula for the nth term is a_n = 4*3^(n-1)
2. a_n = a1*r^(n-1), so a_3 = a_1*r^2 = 1/25, and a_6 = a_1*r^5 = 1/3125
a_6/a_3 = r^3 = 25/3125 = 1/125 -> r = 1/5
Thus a_1 = 1/25/(1/5)^2) = 1
Therefore a_8 = (1/5)^7 = 1/78125
I trust you can complete the other two in a similar fashion...
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