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]