






Last updated at March 9, 2017 by Teachoo
Transcript
Example 14 The sum of first three terms of a G.P. is 13/12 and their product is – 1. Find the common ratio and the terms. Let the three terms in G.P. be 𝑎/𝑟, a, ar here 1st term of G.P. = 𝑎/𝑟 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 And product of first three term = -1 (a/r) × (a) × (ar) = -1 a3 = – 1 a3 = (-1)3 ∴ a = – 1 Putting value of a in (1) a/r + a + ar = 13/12 - 1/r + (-1) + (-1)r = 13/12 - 1/r - 1 – r = 13/12 (− 1 −r −r2)/r = 13/12 (− 1 −r −r2)/r = 13/12 12( -1 – r – r2 )= 13r -12 – 12r – 12r2 = 13r -12 - 12r - 12r2 – 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 12r2 + 25r + 12= 0 where a = 12, b = 25,c = 12, x = r solution of equation is x = (−𝑏 ± √(𝑏2 − 4𝑎𝑐))/29 r = (−25 ± √((25)^2 − 4 × 12 × 12))/(2 × 12) r = (−25 ± √( 625 −576))/24 r = (−25 ± √49)/24 r = (−25 ± 7)/24 r = (−25 ± 7)/24 Now we have a = -1 r = - 3/4 & r = - 4/3 Taking r = - 3/4, a = -1 1st term of G.P. = a/r = (−1)/(−3/4) = 4/3 2nd term of G.P. = a = -1 3nd term of G.P. = ar = (-1)((−3)/4) = 3/4 Hence the three term of G.P. are 4/3, -1, 3/4 Taking r = (−4)/3, a = -1 1st term of G.P. = a/r = (−1)/((−4)/3) = 3/4 2nd term of G.P. = a = -1 3nd term of G.P. = ar = (-1)(4/3) =4/3 Hence the three term of G.P. are 3/4, -1, 4/3 Hence first three terms of G.P. are 3/4, -1, 4/3 for r = (−3)/4 and 3/4, -1, 4/3 for r = (−4)/3
Example 2
Example 3
Example 4
Example 5
Example 6 Important
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14 Important You are here
Example 15 Important
Example 16
Example 17 Important
Example 18 Important
Example 19 Important
Example 20
Example 21 Important
Example 22
Example 23 Important
Example 24 Important
About the Author