Question

The expression n2 + n represents the total number of blocks used in the nth figure of a pattern.

Figure 1 has 2 units. FIgure 2 has 6 units. Figure 3 has 12 units.

Use the equation n2 + n = 56 to determine which figure has 56 blocks.



Figure
has 56 blocks.

Answer 1

Solve n^2 + n = 56:
n^2 + n - 56 = 0
Factor: (n + 8)(n - 7) = 0 → n = 7 or n = -8.

n must be positive, so n = 7.

Figure 7 has 56 blocks.