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

Answer 1

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