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

a1 = 1.an+1 = an + 4.

Problem : Define the arithmetic sequence a1 = 6; an+1 = an - 2 explicitly.

an = - 2n + 8

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

S6 = (a1 + a6) = 3(8 + 18) = 78.

Problem : What is the sum of the first 45 terms in the arithmetic sequence a1 = 3; an+1 = an + 5?

S45 = 45a1 + (45d - d )= 135 + (22.5)(220) = 5085.