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

Question

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

blacksteel · Answer

You'd solve this by simply replacing n with (n+1) everywhere in the equation and then simplifying.

T(n) = 0.5n^2 + 0.5n

T(n+1) = 0.5(n+1)^2 + 0.5(n+1)
=0.5(n^2 + 2n + 1) + 0.5(n+1)
=0.5n^2 + n + 0.5 + 0.5n + 0.5
=0.5n^2 + 1.5n + 1

or (1/2)n^2 + (3/2)n + 1

anonymous · Answer

oh i get it now thx