Answer:
Explanation:
Standard form of a quadratic equation:
Apply same for the quadratic sequence:
Substitute n with 1, 2 and 3 to get the system:
- -1 = a*1² + b*1 + c ⇒ a + b + c = -1
- 5 = a*2² + b*2 + c ⇒ 4a + 2b + c = 5
- 5 = a*3² + b*3 + c ⇒ 9a + 3b + c = 15
Subtract the first equation from the second and subtract the second equation from the third to get:
Again subtract the equations to find a:
Then find b and c:
- b = 3a - 6 = 6 - 6 = 0
- c = -1 - a - b = -1 - 2 - 0 = -3
Substitute the coefficients back into the equation of the quadratic sequence:
- tₙ = 2n² + 0n + (-3) = 2n² - 3