Answer:
The 6th term will be:
[tex]a_6=\frac{729}{16}[/tex]
Step-by-step explanation:
Given
To determine
a₆ = ?
A geometric sequence has a constant ratio r and is defined by
[tex]a_n=a_1\cdot r^{n-1}[/tex]
substituting a₁ = 6, r = 3/2
[tex]a_n=6\cdot \left(\frac{3}{2}\right)^{n-1}[/tex]
Determining 6th term
substituting n = 6 in the given equation
[tex]a_n=6\cdot \left(\frac{3}{2}\right)^{n-1}[/tex]
[tex]a_6=6\cdot \left(\frac{3}{2}\right)^{6-1}[/tex]
[tex]=6\cdot \frac{3^5}{2^5}[/tex]
[tex]=\frac{3^5\cdot \:6}{2^5}[/tex]
[tex]=\frac{3^5\cdot \:2\cdot \:3}{2^5}[/tex]
Cancel the common term
[tex]=\frac{3^6}{2^4}[/tex]
[tex]=\frac{729}{16}[/tex]
Therefore, the 6th term will be:
[tex]a_6=\frac{729}{16}[/tex]
