it p, q, and r are in AP as well as GP , then which one of the following is correct (a) p=q≠r (b) p≠q≠r (c) p≠q=r (d) p=q=r

Asked by varunjoshi2510 | 8th Jan, 2022, 03:08: AM

Expert Answer:

As p, q, r are in A.P., we have
p + r = 2q
i.e. q = (p+r)/2   ... (i)
Since, p, q, r are in G.P., we have
pr = q2
Using (i), we get
pr equals left parenthesis straight p plus straight r right parenthesis squared over 4
rightwards double arrow 4 pr equals straight p squared space plus thin space straight r squared space plus thin space 2 pr
rightwards double arrow 0 equals straight p squared space plus thin space straight r squared space minus 2 pr
rightwards double arrow left parenthesis straight p minus straight r right parenthesis squared space equals space 0
rightwards double arrow straight p equals straight r
rightwards double arrow straight q space equals space left parenthesis straight r plus straight r right parenthesis divided by 2
rightwards double arrow straight q equals straight r
rightwards double arrow straight p equals straight q equals straight r

Answered by Renu Varma | 10th Jan, 2022, 08:30: AM

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