If the \(n\)th term of a quadratic sequence is known, we can work out the terms in that sequence and also use knowledge of solving equations to determine if a specified number is a term in the ...

Terms of a quadratic sequence can be worked out in the same ... put the nth term equal to the number and solve the equation. \(\begin{array}{ccc} 4n + 2 & = & 14 \\ -2 && -2 \end{array}\) ...

The same goes for Catalan numbers, a famous sequence of numbers that describes ... understood to be intimately connected with the quadratic equation,” explained Wildberger.