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Sequences and Series

Problems

Geometric Sequences

How to Cite This SparkNote

Problem : What is the common ratio r in the geometric sequence .5, 1.5, 4.5, 13.5, 40.5,… ?

r = 3 .

Problem : Define the geometric sequence a n = 2×3( n - 1) recursively.

a 1 = 2 ; a n+1 = 3a n .

Problem : Define the geometric sequence a 1 = 4 ; a n+1 = a n explicitly.

a n = 4× ( n - 1)

Problem : What is 53×2( n - 1) ?

S 15 = a 1( = 3() = 3() = 98301 .

Problem : What is the limit of the infinite series 2 + 1 + + + ... ?

a 1 r n-1 = = = 4 .

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