Aim #91: How do we use geometric sequences to solve problems?
Homework: Handout
Do Now: Find the 18th term of -2, 4, -8, ... by writing the explicit formula.
1) The third term of a geometric sequence is 38, and the common ratiois -1/2. Find
the first term.
2) One term of a geometric sequence is a4 = 12. The common ratio is r = 2. Write
the general rule for the nth term.
3) The 5th term of a geometric sequence is 48, and the first term is 3. Find r.
4) A culture of bacteria doubles every 2 hours. If there are 500 bacteria at the
beginning, how many bacteria will there be after 24 hours?
1
5) Given the geometric sequence -5, b, c, 40. Find the values of b and c.
6) Given the geometric sequence 4, a, b, c, 64. Find all possible values ofa, b and c.
7) Find the explicit form of a geometric sequence if f(3) - f(1) = 48 and
.
8) Two terms of a geometric sequence are a3 = -48 and a6 = 3072. Find a rule for
the nth term.
_____, _____, -48, _____, _____, 3072
2
9) Suppose you are given the terms of a geometric sequence a 3 = 27 and a 4 = 81,
find r and a1.
10) Suppose you are given the terms of a geometric sequence a 23 = 16,777,216 and
a24 = 33,554,432, find r and a1.
11) Initially, a pendulum swings through an arc of 18 inches. On eachsuccessive
swing, the length of the arc is 0.98 of the previous length.
a) What is the length of the arc of the 10th swing?
b) On which swing is the length of the arc first less than 12 inches?
Sum It Up!
A geometric sequence has a common ratio.
Recursive: an+1 = (an ) r, a1 = #
Explicit: an = (a1)rn-1 , n≥1
3
HW #91 Answers:
1. an+1 = 1/3an, a1 = 1452 - geometric
2. an = 16(3/4)n-1, 2.8 inches, n ≥ 1
3. an = 54(1/3)n-1 n ≥ 1
4. a = -6, b = 18
5. f(n) = 2(4)n-1 or f(n) = 2(-4)n-1 n ≥ 1
6. an = 1(4)n-1 or an = -1(-4)n-1 n ≥ 1, a4 = 64
7. a = 9 or -9, b = 27, c = 81 or -81
Mixed Review:
1. Addition Prop. of Equality
2. x = 11/6
4