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Tushar Watts Grade: 12
        

Ques) Let a1,a2,a3,..... be in A.P and ap, aq, a be in G.P.  Then show that ap / aq = (q-p) / (r - q).

7 years ago

Answers : (1)

Pratham Ashish
17 Points
										

since, ap,aq & ar are d terms taken from the given A.P.


so,   ap = aq - (q-p)*d ..............................(1)


         aq = ar - (r-q)*d..........................(2)


      now since ap,aq & ar are in G.P. so aq = R*ap


                                                 and, ar = R*aq, where R is d common ratio of tge G.P.


  we put  aq = R*ap in (1)  we get


                                                              ap( R-1) =   (q-p)d  ............................................(3)


we put ar = R* aq in (2)   we get


                                                              aq (R-1) = (r-p) d       .............................................(4)


                                              

dividing  (3) by (4) we get


                                    ap/aq = (q-p)/ (r-p)

7 years ago
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