Introduction to Geometric Sequences NAME_________________________ HOUR_________
Find the common ratio, the next three terms in the following sequences
A: 1, 3, 9… B: 256, 128, 64,… C: 2.7, 3.51, 4.563… D:
−3
8
3
,
20
,
−3
50
,…
If I knew that a particular sequence had a common ratio ‘r’, how would I calculate the ‘n th ’ term? –Write this in recursive form.
Consider the geometric sequence 729, 2187, 6561,… What are the similarities and differences in the sequence compared to the sequence A?
Let 𝐴 𝑛
represent the nth term in an geometric sequence. We know 𝐴
1
= 1, 𝐴
2
= 3, 𝐴
3
= 9 and so on. Write out a recursive formula for sequences A-D.
A) B) C) D)
For problem A what if I wanted to know the 19 th term or 𝐴
19
. Do you really want to write out all 19 terms to find out what it is? I thought not. How can you use the common ratio of the geometric sequence, the first term and the term placement in some way to find the value?
Now put on your big people math pants and Write an Explicit equation that will help us find any value in a geometric sequence.
B) C) D) A)
Find each value
A
A
25
-5
=
=
B
17
=
B
-2
=
C
18
=
C
-3
=
D
40
=
D
-4
=
A term is given for each sequence, find the value for n in corresponding to each term
A n
=1594323, n= B n
= 0.0625, n= C n
=1905.23 , n= D n
= -0.001536, n= A n
=50000, n=
(Careful…)
1.
If the 11 th term’s value in a geometric sequence was 27, with a common ratio of 1.2 what would be the first term?
2.
If the first term is 2.3 and the common ratio is 4.5, what term in the sequence will have 85943.97 as it’s value?

3.
If -262.144 is the 8th term and the first term was 1250 what is the common ratio in the sequence?
4.
Find the 18 th term in the sequence in which A
1
= -27 and r=2.7
5.
Find the number of the term in the sequence in which A n
= -546.75, A
1
=32 and r=-1.5
6.
Find the common ration if A
1
= 27 and A
7
=12
7.
Find the first term in the sequence for which r = .75 and A
11
=4920.75
8.
Find A
1
if r = 5/2 and A
20
=34924596.55.
9.
Find the 15 th term if the sequence is 8, 9.6, 11.52, …
If you were place one grain of rice on a square of a chess board, two grains on a second square, 4 grains on the third and so on; how many grains would there be on each of the following squares…
10.
15 th square
11.
40 th square
12.
64 th square
13.
Which square would have 2097152 grains of rice?
14.
Which square would have 5.6x10
14 grains of rice?
15.
How many grains of rice would it take to fill the board? S=
16.
If there are 29,000 grain of rice in a pound and 475,000,000 tons of rice eaten in the world each year, how long will the chess board feed the world?

Answers
A
A
25
-5
= 2.8E11
= 0.001
B
17
= 0.0039
B
-2
= 2048
A n
=1594323, n=14 B n
= 0.0625, n=13
1.
4.3
2.
8
3.
-0.8
4.
-581497370
5.
8
6.
0.873
7.
87381.33
8.
0.96 or 24/25
9.
102.713
10.
16384
11.
5.49E11
12.
9.22E18
13.
21
14.
50
15.
1.844E19
16.
670 years
C
18
= 233.56
C
-3
= 0.94
C n
=1905.23 , n=26
D
40
= 1.13E-16
D
-4
= -36.6
D n
= -0.001536, n=7 A n
=50000, n= ⦸