19M.1.AHL.TZ2.H_1

pestleMathematicsAIHLPaper 119M· sl-1-2-arithmetic-sequences-and-seriessource ↗

In an arithmetic sequence, the sum of the 3rd and 8th terms is 1.

Given that the sum of the first seven terms is 35, determine the first term and the common difference.

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

attempting to form two equations involving ${u_1}$ and $d$ M1

$\left( {{u_1} + 2d} \right) + \left( {{u_1} + 7d} \right) = 1$ and $\frac{7}{2}\left[ {2{u_1} + 6d} \right] = 35$

$2{u_1} + 9d = 1$

$14{u_1} + 42d = 70\,\,\,\left( {2{u_1} + 6d = 10} \right)$ A1

Note: Award A1 for any two correct equations

attempting to solve their equations: M1

${u_1} = 14$ , $d = - 3$ A1

[4 marks]

Examiners’ report

[N/A]