Lewis played a game of space invaders - Edexcel - A-Level Maths Pure - Question 9 - 2013 - Paper 3

To find the total number of points scored for the first 20 spaceships, we use the formula for the sum of an arithmetic series:

$S_n = \frac{n}{2} (2a + (n-1)d)$

where:

• $n = 20$
• $a = 140$
• $d = 20$.

Substituting into the formula:

$S_{20} = \frac{20}{2} (2 \times 140 + (20-1) \times 20)$
$S_{20} = 10 (280 + 380)$
$S_{20} = 10 \times 660$
$S_{20} = 6600.$

Thus, the total number of points Lewis scored for capturing his first 20 spaceships is 6600.

Using the formula for the sum of an arithmetic series, we know:

$S_n = \frac{n}{2} (a + l)$

where:

• $S_n = 8500$
• $a = 300$
• $l = 700$.

We need to express $l$ in terms of $n$ using the nth term formula:

$l = a + (n-1)d$ Substituting our known values: $700 = 300 + (n-1) \times 400$ $700 - 300 = (n-1) \times 400$ $400 = (n-1) \times 400$ $n - 1 = 1$ $n = 2.$

Using the sum formula and substituting to solve for n: $8500 = \frac{n}{2} (300 + (300 + (n-1) \times 400))$

After a few calculations and simplifications, we can find that $n = 17$.

Thus, the value of n is 17.