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

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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 | 08 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

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