Question

Write an equation for the nth term of the geometric sequence: -12,4,-4/3

I had a_n=-12(3)^(n-1) but that is not a choice on the multiple answers

they have = -12(1/3)^(n-1)
= 12(-1/3)^(n-1)
= -12(-1/3)^(-n+1)
= -12 (-1/3)^(n-1)

Answer 1

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^(n-1)

Just plug in our numbers. The first term is 12, and the common ratio is -1/3.
tn = -12(-1/3)^(n-1)
That's the last option above.