Answer:
80
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
We require to find a₁
Given
a₃ = [tex]\frac{5}{16}[/tex], then
a₁r² = [tex]\frac{5}{16}[/tex], that is
a₁ ×2² = [tex]\frac{5}{16}[/tex] ( divide both sides by 4 )
a₁ = [tex]\frac{5}{64}[/tex], thus
[tex]a_{11}[/tex] = [tex]\frac{5}{64}[/tex] × [tex]2^{10}[/tex] = [tex]\frac{5}{64}[/tex] × 1024 = 5 × 16 = 80
