find the number of terms in the series 20,19 1/3,18 2/3,.... whose sum is 300. explain the double answer.   

Asked by yashwantjain12 | 30th Sep, 2015, 11:18: AM

Expert Answer:

begin mathsize 14px style The space given space sequence comma space 20 comma 19 1 third comma space 18 2 over 3 comma.... space i s space a n space A. P. Given colon space straight S subscript straight n space end subscript equals 300 straight a space equals space 20 comma space straight d space equals space open parentheses 19 1 third minus 20 close parentheses space equals space minus 2 over 3 straight S subscript straight n equals straight n over 2 open square brackets 2 straight a plus open parentheses straight n minus 1 close parentheses straight d close square brackets space space open parentheses Formula close parentheses therefore 300 space equals space straight n over 2 open square brackets open parentheses 2 cross times 20 close parentheses plus open parentheses straight n minus 1 close parentheses open parentheses negative 2 over 3 close parentheses close square brackets therefore 600 equals straight n open square brackets 40 plus open parentheses fraction numerator negative 2 straight n plus 2 over denominator 3 end fraction close parentheses close square brackets therefore 600 equals straight n open square brackets fraction numerator 120 minus 2 straight n plus 2 over denominator 3 end fraction close square brackets therefore 1800 equals 120 straight n minus 2 straight n squared plus 2 straight n space space open parentheses dividing space both space the space sides space by space 2 close parentheses therefore 900 equals 61 straight n minus straight n squared therefore straight n squared minus 61 straight n plus 900 equals 0 therefore open parentheses straight n minus 36 close parentheses open parentheses straight n minus 25 close parentheses equals 0 therefore straight n equals 36 space or space straight n equals space 25 The space double space answers space are space because space this space is space straight a space decreasing space sequence space and space some space terms space are negative. space Hence comma space sum space of space 26 to the power of th space to space 36 to the power of th space terms space is space zero.  space  end style

Answered by Priti Shah | 30th Sep, 2015, 01:13: PM