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in a sequence of (4n+1) terms the first (2n+1) terms are in A.P whose common difference is 2, and the last (2n+1) term are in G.P whose common ratio is 0.5. if the middle terms of the A.P and G.P are equal , then the middle term of the sequence i

in a sequence of (4n+1) terms the first (2n+1) terms are in A.P whose common difference is 2, and the last (2n+1) term are in G.P whose common ratio is 0.5. if the middle terms of the A.P and G.P are equal , then the middle term of the sequence i

Grade:12

2 Answers

Chetan Mandayam Nayakar
312 Points
12 years ago

let m be middle term. m-2n=m(0.5)n,m(1-(0.5)n)=2n,m=2n/((1-(0.5)n))

Sumith Suresh
24 Points
7 years ago
given middle term of ap is = middle term of gp
                       x-2n= x(0.5n)
                       x(1-0.5n) = 2n 
                       
                        x=    2n/(1-0.5n)
                      get rid of the decimal by multipyling 2n/2n
and you get = X = n*2n+1/2n-1

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