How many terms of the AP 18,16,14,12,... are needed to give the sum of 78? Explain the double answer.
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both the answer Will be correct
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AP : 18, 16, 14, 12
Common difference,d = 16-18= -2
Sn= 78
n/2{2a+(n-1)d}=78
n/2{2(18)+(n-1)(-2)}=78
n/2{36-2n+2}=78
n/2{38-2n}=78
19n - n sq. = 78
-n square + 19n - 78 =0
n(-n+13)-6(n+13)=0
(-n+13)(n-6)=0
-n+13=0 or n-6=0
n=6,13
Common difference,d = 16-18= -2
Sn= 78
n/2{2a+(n-1)d}=78
n/2{2(18)+(n-1)(-2)}=78
n/2{36-2n+2}=78
n/2{38-2n}=78
19n - n sq. = 78
-n square + 19n - 78 =0
n(-n+13)-6(n+13)=0
(-n+13)(n-6)=0
-n+13=0 or n-6=0
n=6,13
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