how many terms of the series 54,51,48,......be taken so that their sum is 513?Explain the double answer.
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a=54
d=51-54= -3
sum of n terms=n/2(2a+(n-1)d)=513
n/2(2*54 -3n +3)=513
n/2(108+3 -3n)=513
n/2( 111 -3n)=513
n(111 -3n)=513*2=1026
111n -3n²=1026
3n² -111n +1026=0
⇒n²-37n+342=0
n=19 or 18
d=51-54= -3
sum of n terms=n/2(2a+(n-1)d)=513
n/2(2*54 -3n +3)=513
n/2(108+3 -3n)=513
n/2( 111 -3n)=513
n(111 -3n)=513*2=1026
111n -3n²=1026
3n² -111n +1026=0
⇒n²-37n+342=0
n=19 or 18
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