# Determine the nth term of the arithmetic sequence whose nth partial sum is n2 + 2n. [Hint: The nth term of the sequence is the difference between the sum of the first n terms and the first (n − 1) terms.]

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Determine the nth term of the arithmetic sequence whose nth partial sum is n2 + 2n. [Hint: The nth term of the sequence is the difference between the sum of the first n terms and the first (n − 1) terms.]

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Step 1  help_outlineImage TranscriptioncloseThe nth term of the sequence is the difference between the sum of the first n terms and the first (n – 1) terms. fullscreen
Step 2 ... help_outlineImage TranscriptioncloseThe first (n – 1) th partial sum is (п-1)* +2 (п-1)-(п-1) (n-1+2) - (п-1) (п+1) =n -1 Obtain the difference between the sum of the first n terms and the first (n – 1) terms as n' +2n-(n -1) =n² +2n–n° +1= 2n+1. fullscreen

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MathAlgebra

### Sequence and Series 