Write the first five terms of the sequence a n = n 9 n + 1 a _ { n } = \frac { n } { 9 n + 1 } a n = 9 n + 1 n . Assume that n begins with 1.A) a 1 = − 1 10 , a 2 = − 2 19 , a 3 = − 3 28 , a 4 = − 4 37 , a 5 = − 5 46 a _ { 1 } = - \frac { 1 } { 10 } , a _ { 2 } = - \frac { 2 } { 19 } , a _ { 3 } = - \frac { 3 } { 28 } , a _ { 4 } = - \frac { 4 } { 37 } , a _ { 5 } = - \frac { 5 } { 46 } a 1 = − 10 1 , a 2 = − 19 2 , a 3 = − 28 3 , a 4 = − 37 4 , a 5 = − 46 5 B) a 1 = 1 10 , a 2 = 2 19 , a 3 = 3 28 , a 4 = 4 37 , a 5 = 5 46 a _ { 1 } = \frac { 1 } { 10 } , a _ { 2 } = \frac { 2 } { 19 } , a _ { 3 } = \frac { 3 } { 28 } , a _ { 4 } = \frac { 4 } { 37 } , a _ { 5 } = \frac { 5 } { 46 } a 1 = 10 1 , a 2 = 19 2 , a 3 = 28 3 , a 4 = 37 4 , a 5 = 46 5 C) a 1 = 0 , a 2 = − 1 10 , a 3 = 2 19 , a 4 = − 3 28 , a 5 = 4 37 a _ { 1 } = 0 , a _ { 2 } = - \frac { 1 } { 10 } , a _ { 3 } = \frac { 2 } { 19 } , a _ { 4 } = - \frac { 3 } { 28 } , a _ { 5 } = \frac { 4 } { 37 } a 1 = 0 , a 2 = − 10 1 , a 3 = 19 2 , a 4 = − 28 3 , a 5 = 37 4 D) a 1 = − 1 10 , a 2 = 2 19 , a 3 = − 3 28 , a 4 = 4 37 , a 5 = − 5 46 a _ { 1 } = - \frac { 1 } { 10 } , a _ { 2 } = \frac { 2 } { 19 } , a _ { 3 } = - \frac { 3 } { 28 } , a _ { 4 } = \frac { 4 } { 37 } , a _ { 5 } = - \frac { 5 } { 46 } a 1 = − 10 1 , a 2 = 19 2 , a 3 = − 28 3 , a 4 = 37 4 , a 5 = − 46 5 E) a 1 = 0 , a 2 = 1 10 , a 3 = 2 19 , a 4 = 3 28 , a 5 = 4 37 a _ { 1 } = 0 , a _ { 2 } = \frac { 1 } { 10 } , a _ { 3 } = \frac { 2 } { 19 } , a _ { 4 } = \frac { 3 } { 28 } , a _ { 5 } = \frac { 4 } { 37 } a 1 = 0 , a 2 = 10 1 , a 3 = 19 2 , a 4 = 28 3 , a 5 = 37 4

Question

Write the first five terms of the sequence   a n = n 9 n + 1 a _ { n } = \frac { n } { 9 n + 1 } a n ​ = 9 n + 1 n ​   . Assume that n begins with 1.A)    a 1 = − 1 10 , a 2 = − 2 19 , a 3 = − 3 28 , a 4 = − 4 37 , a 5 = − 5 46 a _ { 1 } = - \frac { 1 } { 10 } , a _ { 2 } = - \frac { 2 } { 19 } , a _ { 3 } = - \frac { 3 } { 28 } , a _ { 4 } = - \frac { 4 } { 37 } , a _ { 5 } = - \frac { 5 } { 46 } a 1 ​ = − 10 1 ​ , a 2 ​ = − 19 2 ​ , a 3 ​ = − 28 3 ​ , a 4 ​ = − 37 4 ​ , a 5 ​ = − 46 5 ​ B)    a 1 = 1 10 , a 2 = 2 19 , a 3 = 3 28 , a 4 = 4 37 , a 5 = 5 46 a _ { 1 } = \frac { 1 } { 10 } , a _ { 2 } = \frac { 2 } { 19 } , a _ { 3 } = \frac { 3 } { 28 } , a _ { 4 } = \frac { 4 } { 37 } , a _ { 5 } = \frac { 5 } { 46 } a 1 ​ = 10 1 ​ , a 2 ​ = 19 2 ​ , a 3 ​ = 28 3 ​ , a 4 ​ = 37 4 ​ , a 5 ​ = 46 5 ​ C)    a 1 = 0 , a 2 = − 1 10 , a 3 = 2 19 , a 4 = − 3 28 , a 5 = 4 37 a _ { 1 } = 0 , a _ { 2 } = - \frac { 1 } { 10 } , a _ { 3 } = \frac { 2 } { 19 } , a _ { 4 } = - \frac { 3 } { 28 } , a _ { 5 } = \frac { 4 } { 37 } a 1 ​ = 0 , a 2 ​ = − 10 1 ​ , a 3 ​ = 19 2 ​ , a 4 ​ = − 28 3 ​ , a 5 ​ = 37 4 ​ D)    a 1 = − 1 10 , a 2 = 2 19 , a 3 = − 3 28 , a 4 = 4 37 , a 5 = − 5 46 a _ { 1 } = - \frac { 1 } { 10 } , a _ { 2 } = \frac { 2 } { 19 } , a _ { 3 } = - \frac { 3 } { 28 } , a _ { 4 } = \frac { 4 } { 37 } , a _ { 5 } = - \frac { 5 } { 46 } a 1 ​ = − 10 1 ​ , a 2 ​ = 19 2 ​ , a 3 ​ = − 28 3 ​ , a 4 ​ = 37 4 ​ , a 5 ​ = − 46 5 ​ E)    a 1 = 0 , a 2 = 1 10 , a 3 = 2 19 , a 4 = 3 28 , a 5 = 4 37 a _ { 1 } = 0 , a _ { 2 } = \frac { 1 } { 10 } , a _ { 3 } = \frac { 2 } { 19 } , a _ { 4 } = \frac { 3 } { 28 } , a _ { 5 } = \frac { 4 } { 37 } a 1 ​ = 0 , a 2 ​ = 10 1 ​ , a 3 ​ = 19 2 ​ , a 4 ​ = 28 3 ​ , a 5 ​ = 37 4 ​

David Greenfield · Accepted Answer

Final Answer : B, Explanation :  We plug in the first few values of $n$ to get $\frac{1}{10}, \frac{2}{19}, \frac{3}{28}, \frac{4}{37}, \frac{5}{46}.$ Thus, the answer is $\boxed{	extbf{(B)}}.$

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