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ICSE Class 10 Answered

The sum of the first 3 terms of GP is 7 and the sum of their squares is 21.  Determine the GP.
Asked by Bidhan | 08 Jun, 2019, 12:49: PM
answered-by-expert Expert Answer
Let space the space first space three space terms space of space GP straight a space space ar space space ar squared straight a space plus space ar space plus ar squared equals 7 straight a open parentheses 1 plus straight r plus straight r squared close parentheses equals 7..... left parenthesis 1 right parenthesis also straight a squared space plus space straight a squared straight r squared space plus straight a squared straight r to the power of 4 equals 21 straight a squared open parentheses 1 plus straight r squared plus straight r to the power of 4 close parentheses equals 21 straight a squared open parentheses 1 plus straight r plus straight r squared close parentheses open parentheses 1 minus straight r plus straight r squared close parentheses equals 21 straight a cross times 7 open parentheses 1 minus straight r plus straight r squared close parentheses equals 21 straight a open parentheses 1 minus straight r plus straight r squared close parentheses equals 3..... left parenthesis 2 right parenthesis fraction numerator left parenthesis 1 right parenthesis over denominator left parenthesis 2 right parenthesis end fraction fraction numerator 1 plus straight r plus straight r squared over denominator 1 minus straight r plus straight r squared end fraction equals 7 over 3 4 straight r squared minus 10 straight r plus 4 equals 0 open parentheses 4 straight r minus 2 close parentheses open parentheses straight r minus 2 close parentheses equals 0 straight r equals 1 half comma 2 straight r equals 2 space straight a equals 1 straight r equals 1 half comma straight a equals 4
Answered by Arun | 08 Jun, 2019, 07:07: PM

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