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20. Sequences, Series & Induction
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Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
20. Sequences, Series & Induction
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20. Sequences, Series & Induction / Geometric Sequences / Problem 5
Problem 5
Using the equation of the nth term of the sequence, evaluate a
2
/a
1
, a
3
/a
2
, a
4
/a
3
and a
5
/a
4
: a
n
= 5(7)
n
.
What do you notice?
A
a
2
/a
1
= a
3
/a
2
= a
4
/a
3
= a
5
/a
4
= 7; The ratio of the term to the term that comes before it is always 7.
B
a
2
/a
1
= 7; a
3
/a
2
= -7; a
4
/a
3
= 7; a
5
/a
4
= -7; The ratio of the term to the term that comes before it is 7, with alternating signs.
C
a
2
/a
1
= a
3
/a
2
= a
4
/a
3
= a
5
/a
4
= 5; The ratio of the term to the term that comes before it is always 5.
D
a
2
/a
1
= 5; a
3
/a
2
= -5; a
4
/a
3
= 5; a
5
/a
4
= -5; The ratio of the term to the term that comes before it is 5, with alternating signs.
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