Check sibling questions

Ex 9.3, 12 - Sum of first three terms of a GP is 39/10 - Geometric Progression(GP): Formulae based

Ex 9.3, 12 - Chapter 9 Class 11 Sequences and Series - Part 2
Ex 9.3, 12 - Chapter 9 Class 11 Sequences and Series - Part 3
Ex 9.3, 12 - Chapter 9 Class 11 Sequences and Series - Part 4
Ex 9.3, 12 - Chapter 9 Class 11 Sequences and Series - Part 5
Ex 9.3, 12 - Chapter 9 Class 11 Sequences and Series - Part 6
Ex 9.3, 12 - Chapter 9 Class 11 Sequences and Series - Part 7

This video is only available for Teachoo black users

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Ex 9.3, 12 The sum of first three terms of a G.P. is 39/10 and their product is 1. Find the common ratio and the terms. 1st term of G.P = / 2st term of G.P = a 3st term of G.P = ar It is given that sum of first three terms = 39/10 i.e. / + a + ar = 39/10 Also, product of first three terms is 1 / a ar = 1 a3 / = 1 a3 = 1 a3 = (1)3 a = 1 putting a = 1 in (1) / + a + ar = 39/10 1/ + 1 + 1(r) = 39/10 (1+ + 2)/ = 39/10 10(1 + r + r2) = 39r 10(1 + r + r2) = 39r 10 + 10r + 10r2 = 39r 10 + 10r + 10r2 39r = 0 10r2 + 10r 39r + 10 = 0 10r2 29r + 10 = 0 The above equation is of the form ax2 + bx + c = 0 Here a = 10 b = -29 c = 10 & x = r Solutions are x = ( ( 2 4 ))/2 r = ( ( 29) (( 29)2 4 10 10))/(2 10) r = ( ( 29) (( 29)2 4 10 10))/(2 10) r = (29 (841 400))/20 r = (29 441)/20 r = (29 ((21)2))/20 r = (29 21)/20 Taking a = 1 & r = 5/2 First term of G.P = / = 1/(5/2) = 2/5 2nd term of G.P = a = 1 3nd term of G.P = ar =1 5/2 = 5/2 Hence first three terms of G.P are 5/2, 1, 5/2 for r = 5/2 Taking a = 1 & r = 2/5 1st term of G.P = / = 1/(2/5) = 5/2 2nd term of G.P = a = 1 3rd term of G.P = ar = 1 2/5 = 2/5 Hence first three term of G.P are 5/2, 1, 2/5 Hence first three term of G.P are 2/5, 1, 5/2 for r = 5/2 & 5/2, 1, 2/5 for r = 2/5

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.