Abby takes 6 steps forward, then 2 steps back. If she repeats this pattern, how many steps will she be from where she started after 4 moves? After 5 moves?
net increase is 4 steps forward. After 4 moves is 16 forward
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To solve this problem, we need to analyze Abby's movement pattern. We know that she takes 6 steps forward and 2 steps back in each cycle. One cycle consists of a forward movement and a backward movement.
After one cycle:
- She moves 6 steps forward.
- She moves 2 steps back.
So, after one cycle, she ends up 6 - 2 = 4 steps forward from where she started.
Now let's calculate her position after multiple cycles:
After 2 cycles:
- She moves 2 cycles forward (6 + 6 steps).
- She moves 2 cycles backward (2 + 2 steps).
So she ends up 4 * 2 = 8 steps forward from where she started.
After 3 cycles:
- She moves 3 cycles forward (6 + 6 + 6 steps).
- She moves 3 cycles backward (2 + 2 + 2 steps).
So she ends up 4 * 3 = 12 steps forward from where she started.
After 4 cycles:
- She moves 4 cycles forward (6 + 6 + 6 + 6 steps).
- She moves 4 cycles backward (2 + 2 + 2 + 2 steps).
So she ends up 4 * 4 = 16 steps forward from where she started.
Finally, after 5 cycles:
- She moves 5 cycles forward (6 + 6 + 6 + 6 + 6 steps).
- She moves 5 cycles backward (2 + 2 + 2 + 2 + 2 steps).
So she ends up 4 * 5 = 20 steps forward from where she started.
Therefore, after 4 moves, Abby will be 16 steps forward from where she started, and after 5 moves, she will be 20 steps forward.