Question

in a GP of positive terms and term is equal to one third of the sum of next two terms.what is the common ratio of the GP​

Answer 1

Answer:

r =  (-1 + √13)/2

Step-by-step explanation:

in a GP of positive terms and term is equal to one third of the sum of next two terms.what is the common ratio of the GP​

Let say GP is

a  , ar   , ar²

term is equal to one third of the sum of next two terms

a = (1/3) ( ar + ar²)

=> 3a = ar( 1 + r)

=> 3 = r ( 1 + r)

=> r² + r - 3 = 0

r = (-1 ± √(1² -4(1)(-3)) )/2

=> r = (-1 ± √13)/2

as r is positive

=> r =  (-1 + √13)/2