Answer:
[tex]T_6 = 37.96875[/tex]
Step-by-step explanation:
Given
[tex]a =5[/tex]
[tex]r = \frac{3}{2}[/tex]
Required
Determine the 6th term
This is calculated as:
[tex]T_n = ar^{n-1[/tex]
Where
[tex]n = 6[/tex]
Substitute [tex]n = 6[/tex], [tex]a =5[/tex] and [tex]r = \frac{3}{2}[/tex]
[tex]T_6 = 5 * (\frac{3}{2})^{6-1[/tex]
[tex]T_6 = 5 * (\frac{3}{2})^{5[/tex]
[tex]T_6 = 5 * (\frac{243}{32})[/tex]
[tex]T_6 = 5 * \frac{243}{32}[/tex]
[tex]T_6 = \frac{5 *243}{32}[/tex]
[tex]T_6 = \frac{1215}{32}[/tex]
[tex]T_6 = 37.96875[/tex]
