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ther is an infinite series with geometric progression, 1st term is the sum of 2nd and 3rd terms, then find the common ratio....

ther is an infinite series with geometric progression,  1st term is the sum of 2nd and 3rd terms,  then find the common ratio....

Grade:9

1 Answers

vikas askiitian expert
509 Points
10 years ago

let geometric series is , a , ar  , ar2 , ar2 ................ infinity

first term is sum of 2nd & third term

a = ar + ar2

r2+r-1 = 0  or        ................1

ax2+bx+c           ............2

this is quadratic equation & its solution is given by dharacharya rule

x = [-b+(-)(b2-4ac)1/2]/2a

a = 1 , b = 1 , c=-1                (on comparing both equations)

x = (root5 - 1)/2     or  -(root5 + 1)/2

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