Higher June 2023 Paper 3 Q13
13 An expression for the \(n\)th term of the sequence of triangular numbers is \(\dfrac{n(n + 1)}{2}\)
Prove that the sum of any two consecutive triangular numbers is a square number. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| Proof | M1 | for giving a general term for a consecutive triangular number eg \(\dfrac{(n + 1)(n + 2)}{2}\) or \(\dfrac{(n - 1)n}{2}\) |
| M1 | for \(\dfrac{n(n + 1)}{2} + \dfrac{(n + 1)(n + 2)}{2}\) or \(\dfrac{(n - 1)n}{2} + \dfrac{n(n + 1)}{2}\) oe | |
| C1 | for completing the proof to show a square number, eg \((n + 1)^2\) or \(n^2\) |