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

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)
```
8 years ago
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