SOLUTION: {1}find the sum of this geometric progression series 16+1\4+___as far as the 6th term????????{2}find the sum of this arithmetic progression 13.9+___+{-0.5}+{-2.1}+{-3.7}
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Question 104065: {1}find the sum of this geometric progression series 16+1\4+___as far as the 6th term????????{2}find the sum of this arithmetic progression 13.9+___+{-0.5}+{-2.1}+{-3.7}
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
{1}find the sum of this geometric progression series 16+1\4+___as far as the 6th term????????{2}
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a(1)=16
d= (1/4)-16 = (-63/4)
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So a(6)= a(1)+5d
a(6) = 16 +5(-63/4) = -62.75
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Then S(6) = (6/2)(a(1)+a(6))
S(6) = 3(16-62.75)= -140.25
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find the sum of this arithmetic progression 13.9+___+{-0.5}+{-2.1}+{-3.7}
a(1)=13.9
d=-1.6
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Determine the order of -3.7
a(n)=13.9+(n-1)(-1.6)
-3.7=13.9-1.6n+1.6
n=12
so -3.7 is the 12th term of the series.
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Add the 1st 12 terms:
S(12)=(12/2)(13.9-3.7)
S(12)=6(10.2)
S(12) = 61.2
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Cheers,
Stan H.
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