IB Maths AI SL 1.2 Arithmetic sequences and series: practice questions

(a) Mark scheme

• (M1) substituting into the term formula, \(13 + (38 - 1) \times 5\);
• A1 \(u_{38} = 198\);

A model answer: \(u_{38} = 13 + (38 - 1) \times 5 = 13 + 185 = 198\)

(b) Mark scheme

• (M1) substituting into the sum formula, \(\frac{n}{2}(2 \times 13 + (n - 1) \times 5) = 5302\);
• (A1) \(\frac{n}{2}(5n + 21) = 5302\) OR \(5n^2 + 21n = 10604\);
• A1 \(5n^2 + 21n - 10604 = 0\);

A model answer: \(S_n = \frac{n}{2}(2 \times 13 + (n - 1) \times 5) = \frac{n}{2}(5n + 21)\).
\(\frac{n}{2}(5n + 21) = 5302 \Rightarrow 5n^2 + 21n = 10604 \Rightarrow 5n^2 + 21n - 10604 = 0\)

(c) Mark scheme

• (M1) an attempt to solve their quadratic: polynomial solver, graph or quadratic formula;
• A1 \(n = 44\);

A model answer: Solving \(5n^2 + 21n - 10604 = 0\) gives \(n = 44\) or \(n = -48.2\). As \(n\) counts terms, \(n = 44\).