1.3 Geometric Sequences
Quiz today!!
Investigate:
A spider’s web is an impressive architectural feat. The following graphic was
created to represent an approximation of the geometric sequence formed by the
orb web.
The capture spiral is constructed
by the spider starting on the
outside edge of the web frame,
and winding inward toward the
hub. The lengths of the sections
of the silk between the radii for
this section of the spiral produce
a geometric sequence. What
makes this sequence geometric?
A geometric sequence: the ratio of consecutive terms is constant.
Each term in the sequence is generated by multiplying by a common ratio.
Ex. Determine the common ratio:
a) 1, 3, 9, 27, ...
b) 12, 6, 3, 1.5, ...
c) 3, -12, 48, -192
d) 2x, 4x2, 8x3, 16x4,
...
Ex. Is 2x, 3x, 4x, 5x, … a geometric sequence?
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Ex. Determine the 6th term of the geometric sequence 2, 6, 18, ...
In general, given a, ar, ar 2, ar3, ar4, ...
The term in the nth positon is
tn = a · rn-1
tn =the nth term (general term)
a = first term
r = common ratio
Ex. Find t10 for 27, 36, 48...
Ex. Find t15 for 50, 30, 18...
Ex. Determine the common ratio of the geometric sequence given t3 = 7 and t6 = -189
Ex. In a geometric sequence the first term is 3.2 and the fifth term is 259.2.
Find the common ratio.
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Ex. In a geometric sequence the first term is 3.2 and the fifth term is 259.2.
Find the common ratio.
**In general, if the common ratio has an even power, there will be 2 possible answers (positive and negative)**
34 = 81
as does (-3)4 = 81
Ex. A battery loses 2% of its charge each day. If the battery is 100% charged today,
how much charge will be left on day 10?
Ex. A baby snake grows at a rate of 5% per day. If it starts out at 30cm, how
* "after 10 days, after 5 bounces, after 4 washes". This is the n+1th term.
long is it after 10 days?
Ex. Given t1 = 4 , r = 4 and tn = 4096. Find the number of terms.
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Assignment: Sec. 1.3: p39 # 1abcde,2ab,3ac, 4, 5, 6ac, 9,10,12,18,19*
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