Look at the pentagonal numbers. Use finite differences to determine which function represents the pattern.

The pentagonal numbers begin 1, 5, 12, 22, 35. Their first differences are 4, 7, 10, 13, so the second differences are all 3. A quadratic with second difference 3 has leading coefficient 3 ÷ 2 = 1.5; the formula that fits the sequence is f(x) = 1.5x² − 0.5x, choice C.

AI-written and checked against the verified answer.