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Example 14 - Sum of first three terms of GP is 13/12, product

Example 14 - Chapter 9 Class 11 Sequences and Series - Part 2
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Example 14 The sum of first three terms of a G.P. is 13/12 and their product is โ€“ 1. Find the common ratio and the terms. Let the three terms in G.P. be ๐‘Ž/๐‘Ÿ, a, ar here 1st term of G.P. = ๐‘Ž/๐‘Ÿ 2nd term of G.P. = a 3rd term of G.P. = ar It is given that Sum of first three terms of G.P. = 13/12 i.e. a/r + a + ar = 13/12 (โˆ’ 1 โˆ’r โˆ’r2)/r = 13/12 12( -1 โ€“ r โ€“ r2 )= 13r -12 โ€“ 12r โ€“ 12r2 = 13r -12 - 12r - 12r2 โ€“ 13r = 0 -12 - 25r - 12r2 = 0 -(12 + 25r + 12r2)= 0 12r2 + 25r + 12= 0 This equation is of the form ax2 + bx + c = 0 where a = 12 b = 25 c = 12 & x = r

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.