Question

A geometric secquence has: a3= 15 a6= 5/27; find common ratio

Answer 1

a=5 while other a is 0.03

Answer 2

Explanation:

`a_(n)=a_(1)*r^(n-1)\\\\a_(3) = 15`

`a_(1)*r^(3-1)=15\\\\a_(1)r^(2)=15 -------------------------------------(I)\\\\a_(6) = (5)/(27)\\\\a_(1) *r^(6-1)=(5)/(27)\\\\a_(1)r^(5)=(5)/(27)-----------------------(II)\\`

(II) ÷ (I)

`(a_(1)r^(5))/(a_(1)r^(2))=((5)/(27))/(15)\\\\\\r^(3)=(5)/(27)*(1)/(15)\\\\r^(3)=(1)/(27*3)\\\\r^(3)=(1)/(81)\\\\r=(1)/(3√(3))`