Answer:
see explanation
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
Here a = 15, thus
[tex]a_{5}[/tex] = 15[tex](r)^{4}[/tex] = [tex]\frac{243}{125}[/tex] ( divide both sides by 15 )
[tex]r^{4}[/tex] = [tex]\frac{243}{1875}[/tex], thus
r = [tex]\sqrt[4]{\frac{243}{1875} }[/tex] = [tex]\frac{3}{5}[/tex]
Multiply the previous term by [tex]\frac{3}{5}[/tex] to obtain the next term
15 × [tex]\frac{3}{5}[/tex] = 9
9 × [tex]\frac{3}{5}[/tex] = [tex]\frac{27}{5}[/tex]
[tex]\frac{27}{5}[/tex] × [tex]\frac{3}{5}[/tex] = [tex]\frac{81}{25}[/tex]
[tex]\frac{81}{25}[/tex] × [tex]\frac{3}{5}[/tex] = [tex]\frac{243}{125}[/tex]
Thus the sequence is
15, 9, [tex]\frac{27}{5}[/tex], [tex]\frac{81}{25}[/tex], [tex]\frac{243}{125}[/tex]
