How many terms of the a.p 16,14,12.....are needed to give the sum 60? Explain why do we get two answers l got ans 5and 12 plz explain why we get two answers
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your answer is correct.
_______________________________
AP=16,14,12,..........
[a=16] , d=[14-16]
= -2
Sn=n/2 [2a+(n-1) d]
now,,,
60=n/2 [2×16+(n-1)-2]
60=n/2 (32-2n+2)
120=32n-2n*+2n
60=16n-n*+n (on dividing by 2)
17n-n*=60
n*-17n+60=0 [make a Quadratic Eqn.]
n*-(12+5) n+60=0
n*-12n-5n+60=
n (n-12) -5 (n-12)=0
(n-12)(n-5)=0
n-12=0 or n-5=0
(n=12) or (n=5)
_______________________________
AP=16,14,12,..........
[a=16] , d=[14-16]
= -2
Sn=n/2 [2a+(n-1) d]
now,,,
60=n/2 [2×16+(n-1)-2]
60=n/2 (32-2n+2)
120=32n-2n*+2n
60=16n-n*+n (on dividing by 2)
17n-n*=60
n*-17n+60=0 [make a Quadratic Eqn.]
n*-(12+5) n+60=0
n*-12n-5n+60=
n (n-12) -5 (n-12)=0
(n-12)(n-5)=0
n-12=0 or n-5=0
(n=12) or (n=5)
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