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ICSE Class 10 Answered

The sum of the first three terms of a G.p is 13/12 and their product is -1.Find the G.p?
Asked by anandarajgowri | 24 Jul, 2018, 08:36: PM
answered-by-expert Expert Answer
Let terms of the geometric progression are begin mathsize 16px style straight a over straight r comma space straight a comma space ar end style
begin mathsize 16px style straight a over straight r plus straight a plus ar equals 13 over 12 rightwards double arrow straight a open parentheses 1 over straight r plus 1 plus straight r close parentheses equals fraction numerator begin display style 13 end style over denominator begin display style 12 end style end fraction......... left parenthesis straight i right parenthesis and fraction numerator begin display style straight a end style over denominator begin display style straight r end style end fraction cross times straight a cross times ar equals negative 1 rightwards double arrow straight a cubed equals negative 1 rightwards double arrow straight a equals negative 1 Put space in space left parenthesis straight i right parenthesis rightwards double arrow fraction numerator begin display style 1 end style over denominator begin display style straight r end style end fraction plus 1 plus straight r equals negative fraction numerator begin display style 13 end style over denominator begin display style 12 end style end fraction rightwards double arrow fraction numerator begin display style 1 end style over denominator begin display style straight r end style end fraction plus straight r equals negative fraction numerator begin display style 13 end style over denominator begin display style 12 end style end fraction minus 1 Solving space further space we space get rightwards double arrow fraction numerator 1 plus straight r squared over denominator straight r end fraction equals fraction numerator negative 25 over denominator 12 end fraction rightwards double arrow 12 plus 12 straight r squared equals negative 25 straight r rightwards double arrow 12 straight r squared plus 25 straight r plus 12 equals 0 rightwards double arrow 12 straight r squared plus 16 straight r plus 9 straight r plus 12 equals 0 rightwards double arrow 4 straight r open parentheses 3 straight r plus 4 close parentheses plus 3 open parentheses 3 straight r plus 4 close parentheses equals 0 rightwards double arrow open parentheses 3 straight r plus 4 close parentheses open parentheses 4 straight r plus 3 close parentheses equals 0 rightwards double arrow straight r equals fraction numerator negative 4 over denominator 3 end fraction space space or space space straight r equals fraction numerator negative 3 over denominator 4 end fraction Find space three space trems space of space an space GP end style
Answered by Sneha shidid | 25 Jul, 2018, 09:24: AM
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ICSE 10 - Maths
in a gp find the tenth term and the sum of first seven terms of 1/2, 1/3, 2/9...
Asked by sudeepguptaa | 28 Nov, 2018, 03:12: PM
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ICSE 10 - Maths
The sum of the first three terms of a G.p is 13/12 and their product is -1.Find the G.p?
Asked by anandarajgowri | 24 Jul, 2018, 08:36: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
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