Algebra 2
posted by Chelsey on .
Write an equation for the nth term of the geometric sequence: 12,4,4/3
I had a_n=12(3)^(n1) but that is not a choice on the multiple answers
they have = 12(1/3)^(n1)
= 12(1/3)^(n1)
= 12(1/3)^(n+1)
= 12 (1/3)^(n1)

We're dividing by 3, so r (the common ratio) is 1/3. The 1/3 is the number by which we're multiplying the previous term. The common ratio always has to be the number that is MULTIPLIED to get the next term. In this example, (12)(1/3) = 4 and 4(1/3) = 4/3.
The formula for calculating the nth term in a geometric sequence is...
tn = t1 . r^(n  1)
the nth term = the first term * the common ratio^(n1)
Just plug in our numbers. The first term is 12, and the common ratio is 1/3.
tn = 12(1/3)^(n1)
That's the last option above.