A video game has been developed whereby the player must earn a certain number of experience points before progressing to the next level.
On level 1, a player must earn 1 experience point.
On level 2, a player must earn 4 experience points.
On level 3, a player must earn 8 experience points.
On level 4, a player must earn 13 experience points.
How many experience points must a player earn on level 7?
13+6+7+8
67
To find out how many experience points a player must earn on level 7, we need to observe the pattern in the given information.
From the given information, we can see that the experience points required for each level follow a pattern where the difference between consecutive levels increases by one each time.
On level 1, a player must earn 1 experience point.
On level 2, a player must earn 4 experience points, which is 1 + 3 (where 3 is the difference between levels 1 and 2).
On level 3, a player must earn 8 experience points, which is 4 + 4 (where 4 is the difference between levels 2 and 3).
On level 4, a player must earn 13 experience points, which is 8 + 5 (where 5 is the difference between levels 3 and 4).
To find the experience points required for level 7, we need to continue this pattern. The difference between levels 4 and 5 is 6, the difference between levels 5 and 6 is 7, and the difference between levels 6 and 7 is 8.
Starting from the previous data point (13 experience points on level 4), we can add 5 (the difference between levels 3 and 4), 6 (the difference between levels 4 and 5), 7 (the difference between levels 5 and 6), and 8 (the difference between levels 6 and 7) successively:
13 + 5 + 6 + 7 + 8 = 39
Therefore, a player must earn 39 experience points on level 7.