Answer:
r = [tex]\frac{7}{8}[/tex]
Step-by-step explanation:
the sum to infinity of a geometric progression is
S∞ = [tex]\frac{a_{1} }{1-r}[/tex] : | r | < 1
where a₁ is the first term and r the common ratio
given S∞ = 8a₁ , then
[tex]\frac{a_{1} }{1-r}[/tex] = 8a₁ ( multiply both sides by 1 - r )
[tex]a_{1}[/tex] = 8a₁(1 - r) ( divide both sides by 8a₁ )
[tex]\frac{a_{1} }{8a_{1} }[/tex] = 1 - r
[tex]\frac{1}{8}[/tex] = 1 - r ( subtract 1 from both sides )
[tex]\frac{1}{8}[/tex] - 1 = - r
[tex]\frac{1}{8}[/tex] - [tex]\frac{8}{8}[/tex] = - r
- [tex]\frac{7}{8}[/tex] = - r ( multiply both sides by - 1 ) , then
r = [tex]\frac{7}{8}[/tex]
