The 4th and 8th term of a G.P. are 24 and 8/27 respectively. find the 1st term and common ratio
Accepted Solution
A:
Answer:see explanationStep-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 ratiogiven a₄ = 24, thena₁[tex]r^{3}[/tex] = 24 → (1)Given a₈ = [tex]\frac{8}{27}[/tex], thena₁[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 = 24a₁ × [tex]\frac{1}{27}[/tex] = 24, hencea₁ = 24 × 27 = 648