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Ques) Let a 1 ,a 2 ,a 3 ,..... be in A.P and a p , a q , a r be in G.P. Then show that ap / aq = (q-p) / (r - q).

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).

Grade:12

1 Answers

Pratham Ashish
17 Points
12 years ago

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)

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