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T(n) is the total number of lights in a triangular lighting rig of n rows, as shown. Which polynomial function represents T(n + 1)? T(n)=1/2n^2+1/2n a. T(n+1)=1/2n^2+3/2n+1 b. T(n+1)=1/2n^2+1/2n+1 c. T(n+1)=1/2n^2+n+1
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Aug 19, 2017
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T(n) is the total number of lights in a triangular lighting rig of n rows, as shown. Which polynomial function represents T(n + 1)?
T(n)=1/2n^2+1/2n
a. T(n+1)=1/2n^2+3/2n+1
b. T(n+1)=1/2n^2+1/2n+1
c. T(n+1)=1/2n^2+n+1
d. T(n+1)=1/2n^2+1
Mathematics
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Fotini
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The answer is
a. T(n+1)=1/2n^2+3/2n+1
T(n) = 1/2n² + 1/2n = 1/2(n² + n)
T(n + 1) = 1/2((n+1)² + (n+1))
(a + b)² = a² + 2ab + b²
(n + 1)² = n² + 2n + 1
T(n + 1) = 1/2(n² + 2n + 1 + n + 1) =
= 1/2(n² + 3n + 2) =
= 1/2n² + 3/2n + 1
JoaoCC
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Aug 23, 2017
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JoaoCC
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