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in a G.P. of positive numbers, any term is equal to the sum of hte next two terms. the common ratio of the G.P. is-

in a G.P. of positive numbers, any term is equal to the sum of hte next two terms. the common ratio of the G.P. is-

Grade:12

1 Answers

Amit Jain
askIITians Faculty 32 Points
7 years ago

Let the first term be a and Common ration be r.

 

Tn = Tn+1 + Tn+2

ar^n-1 = ar^n + ar^n+1

1= r + r ^2

On solving the quadratic equation,

 

r= (√5 - 1)/2 (The negative answer rejected as the GP is of positive numbers)

 

 

 

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