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Grade: 11

                        

If pth,qth,rth terms on an ap are in GP find the common ratio.

2 years ago

Answers : (1)

Arun
24738 Points
							
Dear student
 
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
2 years ago
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