Question

Find the exact value of the 8th term of the geometric sequence: 648,216,72,24

a) .30

b) 8
___
2481

c) 8
___
9

d) 8
___
27

Answer 1

The sequence multiplies by 1/3.
Using the formula for a geometric sequence:
a(n) = a(1) * r^(n-1)
So...
a(n) = 648 * (1/3)^(n-1)
Plugging in 8 for n produces:
a(n) = 648 * (1/3)^(7)
Using a calculator, I find the answer to be 0.296296296...