Respuesta :

Given:

The sequence is:

[tex]a_n=\frac{1}{7+2n}[/tex]

The first term

[tex]a_1=\frac{1}{9}[/tex]

Required:

Find the common difference of the sequence.

Explanation:

The given sequence is

[tex]\begin{gathered} a_{n}=\frac{1}{7+2n} \\ a_1=\frac{1}{9} \end{gathered}[/tex]

Substitute n = 2

[tex]\begin{gathered} a_2=\frac{1}{7+2(2)} \\ a_2=\frac{1}{7+4} \\ a_2=\frac{1}{11} \end{gathered}[/tex]

Substitute n = 3

[tex]\begin{gathered} a_3=\frac{1}{7+2(3)} \\ a_3=\frac{1}{7+6} \\ a_3=\frac{1}{13} \end{gathered}[/tex]

Thue the numbers of the sequence are:

[tex]\frac{1}{9},\frac{1}{11},\frac{1}{13},....[/tex]

The given sequence is in HP.

Write it in AP as:

[tex]9,11,13[/tex]

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