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If pth,qth,rth, Doremon AP are in GP find the common ratio.

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2 years ago

Arun
25768 Points
```							Let first term of the AP = a and common difference = d pth of an AP= a+(p−1)d qth of an AP= a+(q−1)d rth of an AP= a+(r−1)d are in G.P Let first term of the GP be x and common ratio be y then a+(p−1)d=x........(i) a+(q−1)d =xy........(ii) a+(r−1)d=xy² ........(iii) Subtract (i) from (ii) and get (q−1)d −(p−1)d=xy−x →(q−p)d=xy−x......(iv) Subtract (ii) from (iii) and get (p−1)d −(r−1)d=xy²−xy =y(xy−x) →(q−r)d=y(xy−x) .....(v) divide (v) by (iv) and get (q−r)/(p−q)= y RegardsArun (askIITians forum expert)
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2 years ago
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