Question

The 4th and 8th term of a G.P. are 24 and 8/27 respectively. find the 1st term and common ratio

Answer 1

Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric progression is

• $a_{n}$ = a₁ $r^{n-1}$

where a₁ is the first term and r the common ratio

given a₄ = 24, then

a₁$r^{3}$ = 24 → (1)

Given a₈ = $\frac{8}{27}$, then

a₁$r^{7}$ = $\frac{8}{27}$ → (2)

Divide (2) by (1)

$r^{4}$ = $\frac{\frac{8}{27} }{24}$ = $\frac{1}{81}$

Hence r = $\sqrt[4]{\frac{1}{81} }$ = $\frac{1}{3}$

Substitute this value into (1)

a₁ × ($\frac{1}{3}$ )³ = 24

a₁ × $\frac{1}{27}$ = 24, hence

a₁ = 24 × 27 = 648