precal question

Question

Find the indicated term of the geometric sequence with the given description.

The first term is 1/6

and the second term is − 1/2

.

 Find the sixth term.

Answer 1

The common ratio (the multiplier) is calculated by 1/6x = -1/2 or x = (1/2)/(-1/6) = (1/2)•(-6/1) = -3.

The equation of the sequence would be a_n = (-1/18)*(-3)ⁿ (or an = (1/6)(-3)^n-1 - both give the same result)

The 6th term (n = 6) is a₆ = (-1/18)*(-3)⁶ = -40.5

Or you could use the recursive method:

Term Term

# Value

-----------------

1 1/6

2 -1/2

3 1.5

4 -4.5

5 13.5

6 -40.5