Aim #90: How do we use geometric sequences to solve problems?
4-24-17
Homework: Handout
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Do Now: Find the 18 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
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the general rule for the n 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?
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
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.
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a) What is the length of the arc of the 10 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.
n-1
Recursive: an+1 = (an ) r, a1 = #
Explicit: an = (a1)r , n≥1