Aim #90: What is a geometric sequence?
Homework: Handout
Do Now: Write the recursive formula and find the next term for:
a. 3, 15, 75, ...
b. -1, 6, -36, ...
A geometric sequence is a sequence in which the quotient of each termand the
preceding term is the same constantr.
3, 6, 12, 24, . . .
What is the constant r? How did you determine it?
Write the recursive and explicit formula.
Explicit formula for a geometric sequence:
Recursive formula for a
geometric sequence:
an =
an =
1) Determine if each of the following formulas is recursive or explicit and then
write out the first 5 terms. Write the other formula as well.
a. an = 3(2)n-1, n ≥ 1
b. f(n+1) = -4f(n) , f(1) = 2
c. an = 6an-1 , a1 = -4
d. f(n) = -2(.5)n, n ≥ 1
2) Given the following sequences, determine if they are geometricor not. If they
are, find the common ratio and determine a formula to find the nth term.
a. 2, 6, 18, 54, 162, . . .
c. 81, 27, 9, 3, 1, . . .
b. 2, -4, 8, -12, . . .
d.
3) a. If 4, 20, 100, 500, . . ., find the rule for a n .
b. What is the 7th term?
c. What term of the sequence is 195,312,500?
4) a. Given the sequence 4, -12, 36, . . . find the rule for a n .
b. What is the 10th term?
c. Why does the sequence alternate from positive to negative?
5) a. Given the sequence f(n) = .5f(n-1) , f(1) = 9, find the explicit rule for f(n) .
b. What is the 6th term?
Sum It Up!
A geometric sequence has a common ratio.
Recursive: an+1 = (an ) r, a1 = #
Explicit: an = (a1)rn-1 , n≥1