what is the nth term for this quadratic sequence: 7, 10, 15, 22, 31

Find the nth term of a quadratic sequence, we need to identify the pattern. Let's analyze the given sequence:1. 7 = 72. 10 = 7 + 33. 15 = 7 + 84. 22 = 7 + 155. 31 = 7 + 24The differences between consecutive terms are increasing quadratically:+3, +5, +7, +9, ...We can represent the sequence using the quadratic formula:an = a + (n-1)d + (n-1)(n-2)cwhere:a = 7 (first term)d = 3 (initial difference)c = 1 (constant increase in difference)Simplifying, we get:an = 7 + 3(n-1) + (n-1)(n-2)an = 7 + 3n - 3 + n² - 3n + 2an = n² + 2The nth term of the sequence is:an = n² + 6Please verify:1. a₁ = 1² + 6 = 72. a₂ = 2² + 6 = 103. a₃ = 3² + 6 = 154. a₄ = 4² + 6 = 225. a₅ = 5² + 6 = 31

Answered by mjPcontiga | 2024-10-21