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Sequences and Series

Problems

Arithmetic Sequences

Geometric Sequences

Problem : Define the arithmetic sequence a n = 4n - 3 recursively.

a 1 = 1.a n+1 = a n + 4 .

Problem : Define the arithmetic sequence a 1 = 6 ; a n+1 = a n - 2 explicitly.

a n = - 2n + 8

Problem : What is the sum of the first six terms of the sequence a n = 2n + 6 ?

S 6 = (a 1 + a 6) = 3(8 + 18) = 78 .

Problem : What is the sum of the first 45 terms in the arithmetic sequence a 1 = 3 ; a n+1 = a n + 5 ?

S 45 = 45a 1 + (45d - d )= 135 + (22.5)(220) = 5085 .

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