Quadratic sequence nth terms

(a) $n^2 + 2n$

• M1 Finding the second difference 2 and the term $n^2$.
• M1 Subtracting $n^2$ to get the linear part $2, 4, 6, \ldots$
• A1 The correct answer, $n^2 + 2n$.

(a) $3n^{2}-n+9$

• M1 Use the second difference to write the form $an^2 + bn + c$.
• M1 Use the two known terms to solve for the linear coefficient and constant.
• A1 Correct answer: $3n^{2}-n+9$

(b) $21$

• M1 The 20th term equals the threshold and all later differences are positive.
• A1 Correct answer: $21$

(a) $30$

• P1 Establishing $2b+c=5$ or an equivalent valid method.
• P1 Establishing $5b+c=17$ or an equivalent valid method.
• P1 Establishing $29^{2}+4\times 29-3$ or an equivalent valid method.
• P1 Establishing $30^{2}+4\times 30-3$ or an equivalent valid method.
• A1 Correct answer: $30$