Answer:
a₇ = [tex]\frac{4096}{3125}[/tex]
Step-by-step explanation:
There is a common ratio r between consecutive terms, that is
r = 4 ÷ 5 = [tex]\frac{4}{5}[/tex]
r = [tex]\frac{16}{5}[/tex] ÷ 4 = [tex]\frac{4}{5}[/tex]
This indicates the sequence is geometric with n th term
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 5 and r = [tex]\frac{4}{5}[/tex] , thus
a₇ = 5 × [tex](\frac{4}{5}) ^{6}[/tex] = 5 × [tex]\frac{4096}{15625}[/tex] = [tex]\frac{4096}{3125}[/tex]
