Lewis played a game of space invaders - Edexcel - A-Level Maths Pure - Question 8 - 2013 - Paper 3

To find the total points scored for the first 20 spaceships, we use the sum formula for an arithmetic series: $S_n = \frac{n}{2} \times (2a + (n - 1)d)$ Where $n = 20$, $a = 140$, and $d = 20$: $S_{20} = \frac{20}{2} \times (2 \times 140 + (20 - 1) \times 20)$ Calculating: $S_{20} = 10 \times (280 + 380) = 10 \times 660 = 6600$ Hence, the total number of points Lewis scored is 6600 points.

Given that Sian captured $n$ dragons and the total points scored was 8500, we can use the sum formula for an arithmetic sequence as before. For Sian, the first term $a = 300$ and the $n^{th}$ term is $700$: Using the formula: $S_n = \frac{n}{2} (a + l)$ Where $l$ is the last term: $8500 = \frac{n}{2} (300 + 700)$ This simplifies to: $8500 = 500n$ Solving for $n$ gives: $n = \frac{8500}{500} = 17$ Thus, the value of n is 17.