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Arindam Paul posted an Question
June 25, 2021 • 16:11 pm
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30 points
30 points
- IIT JAM
- Biotechnology (BT)
A,b,c are in ap, b,c,d are in gp and c,d,e are in hp. what is the relation among a,c,d?
a,b,c are in AP, b,c,d are in GP and c,d,e are in HP. What is the relation among a,c,d?
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Abhijeet Gaurav![best-answer]()
Since a, b, c are in AP 2b = a+c …(i) Since b, c, d are in GP c2 = bd …(ii) Since c, d, e are in HP 2/d = 1/c + 1/e 2/d = (c+e)/ce …(iii) From (ii), d = c2/b Substitute d in (iii) 2b/c2 = (c+e)/ce 2b/c = (c+e)/e (a+c)/c = (c+e)/e ( From (i) ) Cross multiplying, we get ae + ce = c2 + ce ae = c2 So a, c, e are in GP. Hence GP Is the answer.