Question

The total number of lights in a triangular rig with n rows is given by the function T(n) as given. Find the number of lights in triangular rigs with 1 to 10 rows.

T(n)=1/2n^2+1/2n

Answer 1

T(1) = 1/2(1)^2 + 1/2(1) = 1/2 + 1/2 = 1
T(2) = 1/2(2)^2 + 1/2(2) = 1/2(4) + 1 = 2 + 1 = 3
T(3) = 1/2(3)^2 + 1/2(3) = 1/2(9) + 3/2 = 9/2 + 3/2 = 12/2 = 6
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T(10) = 1/2(10)^2 + 1/2(10) = 1/2(100) + 5 = 50 + 5 = 55

Therefore, the number of lights in triangular rigs with 1 to 10 rows are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55