Ex 8.2, 3 The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps. We know that an = arn – 1 where an = nth term of GP n is the number of terms a is the first term r is the common ratio Here, 5th term is p i.e. a5 = p Putting n = 5 in an formula p = ar5–1 p = ar4 Also, 8th term is q i.e. a8 = q Putting n = 8 in an formula q = ar8 – 1 q = ar7 Also, 11th term is s i.e. a11 = s Putting n = 11 in an formula s = ar11 – 1 s = ar10 We need to show that q2 = ps. Taking L.H.S q2 Putting value q = ar7 from (2) = (ar7)2 = a2r14 Now, solving R.H.S ps Putting p = ar4 , s = ar10 from (1)& (3) = (ar4) (ar10) = (a × a)(r10 × r4) = a2r14 = L.H.S Thus, L.H.S = R.H.S Hence proved

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.