Question
Tue July 26, 2011 By:
 

How many terms of A.P. 16,14,12,....are+ needed to give the sum 60? Explain why we get double answer?

Expert Reply
Tue July 26, 2011
16,14,12
sum=n/2{2a+(n-1)d}
60=n/2{2*16+(n-1)(-2)}
120=n{34-2n}
120=34n-2n2
n2 -17n+60=0
n2 -12n-5n+60=0
n(n-12)-5(n-12)=0
n=5,12
here,the common difference is negative therefore terms go on diminishing and 9th term becomes zero.All terms after 9th term are negative.These negative terms when added to positive terms from 6th to 8th term,they cancel out each other and the sum remains same.
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