The sum of an infinite geometric series is 15 and the sum of the squares of the terms is 45. Find the series.

Asked by Olivia Adhikary | 19th Aug, 2014, 11:16: AM

Expert Answer:

fraction numerator a over denominator 1 minus r end fraction equals 15 fraction numerator a squared over denominator 1 minus r squared end fraction equals 45  S u b s t i t u t e space a equals 15 left parenthesis 1 minus r right parenthesis space f r o m space 1 space i n space 2 comma space w e space g e t open square brackets 15 left parenthesis 1 minus r right parenthesis close square brackets squared equals 45 left parenthesis 1 minus r squared right parenthesis 5 left parenthesis 1 plus r squared minus 2 r right parenthesis equals 1 minus r squared 6 r squared minus 10 r plus 4 equals 0 6 r squared minus 6 r minus 4 r plus 4 equals 0 open parentheses 6 r minus 4 close parentheses left parenthesis r minus 1 right parenthesis equals 0 r equals 1 space o r space 2 over 3 space b u t space r not equal to 1 comma space s o space r equals 2 over 3 rightwards double arrow a equals 5  S o space s e r i e s space i s space 5 comma space 10 over 3 comma 20 over 9 comma 40 over 27..... space

Answered by Dharma Teja | 19th Aug, 2014, 03:53: PM

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