Moderate -0.3 This is a straightforward application of standard arithmetic sequence formulas (nth term and sum) with two equations and two unknowns. While it requires setting up and solving simultaneous equations, the algebraic manipulation is routine for A-level students, and the context provides clear structure. Slightly easier than average due to the direct application of formulas with no conceptual challenges.
An athlete prepares for a race by completing a practice run on each of 11 consecutive days. On each day after the first day he runs further than he ran on the previous day. The lengths of his 11 practice runs form an arithmetic sequence with first term \(a\) km and common difference \(d\) km.
He runs 9 km on the 11th day, and he runs a total of 77 km over the 11 day period.
Find the value of \(a\) and the value of \(d\). [7]
An athlete prepares for a race by completing a practice run on each of 11 consecutive days. On each day after the first day he runs further than he ran on the previous day. The lengths of his 11 practice runs form an arithmetic sequence with first term $a$ km and common difference $d$ km.
He runs 9 km on the 11th day, and he runs a total of 77 km over the 11 day period.
Find the value of $a$ and the value of $d$. [7]
\hfill \mbox{\textit{Edexcel C1 Q7 [7]}}