Make a journal of what you have learned about finite geometric sequence and
infinite geometric sequence. State the difference between the two. You can also
include part of the lesson you feel difficult and work on with this difficulty with your
teacher. Give also an example of finite and infinite geometric sequence.
Answers
Geometric sequence
Step-by-step explanation:
Geometric sequence is called geometric progression as well
Next term in Geometric sequence is always obtained by multiplying by a constant term with the term.
that constant term is called common ratio
a , ar , ar² ,...................................arⁿ⁻¹
a = 1st term
r = common ratio
nth term = arⁿ⁻¹
Sum of n terms = a(rⁿ - 1)/(r - 1)
finite geometric sequence will have fixed number of term .
Infinite geometric sequence will have infinite terms
and common ratio would lie between - 1 and 1 so that sequence can converge.
Sum of infinite geometric sequence = a/(1 - r)
finite geometric sequence
1 2 4 8 16
5 15 45 135
3 -6 12 - 24 48 -96
infinite geometric sequence
1 1/2 1/4 1/8 1/6 ....................................
2 -1 1/2 -1/4 1/8 -1/16
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