Question

Find the nth term of this quadratic sequence 4 9 16 25 36

Answer 1

aₙ = n² + 2n + 1

Explanation:

a₁ = 4 = 2² = (1 + 1)²

a₂ = 9 = 3² = (2 + 1)²

a₃ = 16 = 4² = (3 + 1)²

a₄ = 25 = 5² = (4 + 1)²

a₅ = 36 = 6² = (5 + 1)²

Therefore:

aₙ = (n + 1)² = n² + 2n + 1