Answer:
see explanation
Step-by-step explanation:
The n th term of a geometric progression is
• [tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
given a₄ = 24, then
a₁[tex]r^{3}[/tex] = 24 → (1)
Given a₈ = [tex]\frac{8}{27}[/tex], then
a₁[tex]r^{7}[/tex] = [tex]\frac{8}{27}[/tex] → (2)
Divide (2) by (1)
[tex]r^{4}[/tex] = [tex]\frac{\frac{8}{27} }{24}[/tex] = [tex]\frac{1}{81}[/tex]
Hence r = [tex]\sqrt[4]{\frac{1}{81} }[/tex] = [tex]\frac{1}{3}[/tex]
Substitute this value into (1)
a₁ × ([tex]\frac{1}{3}[/tex] )³ = 24
a₁ × [tex]\frac{1}{27}[/tex] = 24, hence
a₁ = 24 × 27 = 648
