Answer:
a₁₁ = 6144
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
Given a₃ = 24 and a₅ = 96 , then
a₁r² = 24 → (1)
a₁[tex]r^{4}[/tex] = 96 → (2)
Divide (2) by (1)
[tex]\frac{ar^4}{ar^2}[/tex] = [tex]\frac{96}{24}[/tex] , that is
r² = 4 , thus
r = 2
substitute r = 2 into (1)
4a₁ = 24 ( divide both sides by 4 )
a₁ = 6
Thus
a₁₁ = 6 × [tex]2^{10}[/tex] = 6 × 1024 = 6144
