Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | January | Q#7

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Question

Lewis played a game of space invaders. He scored points for each spaceship that he captured.

Lewis scored 140 points for capturing his first spaceship. He scored 160 points for capturing his  second spaceship, 180 points for capturing his third spaceship, and so on.

The number of points scored for capturing each successive spaceship formed an arithmetic  sequence.

a.   Find the number of points that Lewis scored for capturing his 20th  spaceship.

b.   Find the total number of points Lewis scored for capturing his first 20 spaceships.

Sian played an adventure game. She scored points for each dragon that she captured. The number  of points that Sian scored for capturing each successive dragon formed an arithmetic sequence. 

Sian captured n dragons and the total number of points that she scored for capturing all n dragons  was 8500. Given that Sian scored 300 points for capturing her first dragon and then 700 points for  capturing her nth dragon, 

c.   find the value of n.

Solution

a.
 

We are given that the points scored by Lewis for capturing each successive spaceship form an  arithmetic sequence.

From the given information we can collect following data about the said arithmetic sequence. 

Expression for difference  in Arithmetic Progression (A.P) is:

Therefore;

We are required to find the points scored for 20th spaceship.

It is evident that we are looking for 20th term of above given arithmetic sequence.

Expression for the general term  in the Arithmetic Progression (A.P) is:

Therefore;

Hence, he scored 520 points on capturing 20th spaceship. 

b.
 

We are required to find the total points scored for capturing first 20 spaceships.

It is evident that we are looking for the sum of 20 terms of above given arithmetic sequence.

Expression for the sum of  number of terms in the Arithmetic Progression (A.P) is:

Therefore;

Hence, his total score after capturing 20 spaceships is 6600.

c.
 

We are given that number of points that Sian scored for capturing each successive dragon form an  arithmetic sequence. 

From the given information we can collect following data about the said arithmetic sequence.

She captured n dragons.

She scored 8500 for capturing all n dragons.

We are required to find n ie total number of terms (dragons).

Expression for the sum of  number of terms in the Arithmetic Progression (A.P) is:

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