Question

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.
Which recursive equation represents the pattern? (2 points)
Select one:
a. an = an - 1 + n
b. an = an - 1 + (n + 1)
c. an = an - 1 + 2n
d. an = an - 1 + (2n + 1)

Answer 1

What is the pattern?
From level 1 to level 2, + ? points
From level 2 to level 3, + ? points
From level 3 to level 4, + ? points

Answer 2

Notice what that pattern is, and it should be clear how it is related to n.

Answer 3

it goes +3,+4,+5

Answer 4

so would it be D?

Answer 5

still need help

Answer 6

D says that: In level n, you take the points from level n-1, and add 2n + 1. So let's see what that would give:

When n=1 you have 1 point.
When n=2 you have the points from n=1 (1) and add 2n + 1, so you would need:
1 + 2(2) + 1 = 6
So that's not it, because you know that for n=1 you should need 4 points, not 6.

Answer 7

Look again at the pattern, you have it correct:

From level 1 to level 2, + ? points you said +3
From level 2 to level 3, + ? points you said +4
From level 3 to level 4, + ? points you said +5

So to get to level 2, meaning, \(\Large \color{red}{n=2}\), you need \(\Large \color{red}3\) more points than at n=1
So to get to level 3, meaning, \(\Large \color{red}{n=3}\), you need \(\Large \color{red}4\) more points than at n=2
So to get to level 4, meaning, \(\Large \color{red}{n=4}\), you need \(\Large \color{red}5\) more points than at n=3

What is the pattern, as it related to n?