Answer:
The nth term of the series is
[tex]a_n=\frac{2}{3}\cdot 6^{n-1}[/tex]
Step-by-step explanation:
Given: Third term = 24 and r = 6
We are given third term and common ratio of geometric series.
Formula:
[tex]a_n=a\cdot r^{n-1}[/tex]
For third term, n=3 and r=6
[tex]a_3=a\cdot 6^{3-1}[/tex]
[tex]24=a\cdot 36[/tex]
[tex]a=\frac{2}{3}[/tex]
We need to find nth term of the series
[tex]a_n=\frac{2}{3}\cdot 6^{n-1}[/tex]
Hence, The nth term of the series is [tex]a_n=\frac{2}{3}\cdot 6^{n-1}[/tex]
