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22-02-2017
Mathematics

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An arithmetic sequence is represented as 5 , 9 , 13 , ... with the nth term represented as 4n + 1. Write a formula to represent the sum of the first n terms.

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LammettHash LammettHash

22-02-2017

Let [tex]a_n=4n+1[/tex].

[tex]S_n=\displaystyle\sum_{k=1}^na_k=\sum_{k=1}^n(4k+1)[/tex]
[tex]S_n=\displaystyle4\sum_{k=1}^nk+\sum_{k=1}^n1[/tex]
[tex]S_n=\displaystyle4\frac{n(n+1)}2+n[/tex]
[tex]S_n=2n^2+3n[/tex]

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