Question

It would take Dave 48 hours to repaint his whole house. If Dave asked a friend to help, it would take them 24 hours. If a third friend helped paint, it would take 12 hours. Is this an arithmetic or geometric sequence? Explain.

Answer 1

The problem can be solved using arithmetic sequences. Each term is obtained by adding a constant difference to the previous term. The solution represents an arithmetic sequence.

Step-by-step explanation:

This problem can be solved using arithmetic sequences. In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. In this case, the number of hours it takes to paint the house decreases by a constant difference each time another friend helps. Let's represent the number of hours it takes for Dave to paint the house alone as 'a', and the constant difference as 'd'.

When Dave paints alone, it takes him 48 hours (a=48). When Dave and his friend paint together, it takes them 24 hours (a+d=24). When three friends paint together, it takes them 12 hours (a+2d=12). To find 'd', we can subtract the second equation from the first equation, and subtract the third equation from the second equation:

(a+d) - a = 24 - 48

(a+2d) - (a+d) = 12 - 24

simplifying these equations gives:

d = -24

d = -12

We have two possible values for 'd', which means there are two possible sequences. However, since negative values of time don't make sense in this context, we can disregard the solution 'd = -24'. Therefore, the sequence that represents the situation is an arithmetic sequence.