Find the value of n if 50+46+42+38+......... To n terms=336
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Since , 46-50=42-46=-4, therefore the given terms are in Arithmatic Progression with a common difference(d)= -4 , and first term(a)=50
Sn=n/2[2a+(n-1)d]
336=n/2[2*50+(n-1)*(-4)]
336*2=n[100-4n+4]
672=104n-4n^2
4n^2-104n+672=0
n^2-26n+168=0
n^2-14n-12n+168=0
n(n-14)-12(n-14)=0
(n-14)(n-12)=0
therefore, n=14 or n=12
Sn=n/2[2a+(n-1)d]
336=n/2[2*50+(n-1)*(-4)]
336*2=n[100-4n+4]
672=104n-4n^2
4n^2-104n+672=0
n^2-26n+168=0
n^2-14n-12n+168=0
n(n-14)-12(n-14)=0
(n-14)(n-12)=0
therefore, n=14 or n=12
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