[tex]\mathbf{19^{th}}[/tex] term of a geometric sequence is 31035.73 and common ratio is 1.5.
General term of a GP is denoted by [tex]a_{n}[/tex] and [tex]$a_{n}=a \cdot r^{n-1}$[/tex]
Given that
[tex]a_{9}=358.80[/tex]
[tex]$a_{1}=14$[/tex]
So common ratio can be calculated as
[tex]a_{9}=a \cdot r^{8}\\[/tex]
[tex]350.80=14 \cdot r^{8}\\[/tex]
[tex]r^{8}=25.6285[/tex]
[tex]r=1.499 \\r \approx 1.5 \\[/tex]
Now [tex]\mathbf{19^{th}}[/tex] term can be calculated as
[tex]a_{19}=14(1.5)^{19} \\a_{19}=31,035.7294 \\a_{19} \approx 31035.73[/tex]
[tex]\mathbf{19^{th}}[/tex] term of a geometric sequence is 31035.73 and common ratio is 1.5
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