Sequences and Series

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

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

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

Solution for Problem 3 >>

a _n = 4× ⁽ n - 1)

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Problem : What is 53×2⁽ n - 1) ?

Solution for Problem 4 >>

S ₁5 = a ₁( = 3() = 3() = 98301 .

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

Solution for Problem 5 >>

a ₁ r ^n-1 = = = 4 .

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