Question

I'm studying for my math test and I'm stuck on a sequence problem. The sequence is -1, 9, 19, 29... and I need to find the next three terms. I also have a friend who's into gardening and he's been telling me about his dahlia plants. Apparently, the bulbs double in number each year, and he had 8 bulbs in the first year.

Answer 1

Let's tackle the sequence first. The given sequence is: -1, 9, 19, 29...

To find the pattern, let's look at the differences between consecutive terms:

- 9 - (-1) = 10
- 19 - 9 = 10
- 29 - 19 = 10

The difference between each term is constant at 10. This means we can find the next terms by continuing this pattern.

- The next term after 29 would be: 29 + 10 = 39
- The term after that would be: 39 + 10 = 49
- Finally, the term after 49 would be: 49 + 10 = 59

Therefore, the next three terms in the sequence are **39, 49, and 59**.

Now, regarding your friend’s dahlia plants: If he starts with 8 bulbs in the first year and the number of bulbs doubles each year, we can find the number of bulbs for each year using the power of 2.

- Year 1: \( 8 \) bulbs
- Year 2: \( 8 \times 2^1 = 8 \times 2 = 16 \) bulbs
- Year 3: \( 8 \times 2^2 = 8 \times 4 = 32 \) bulbs
- Year 4: \( 8 \times 2^3 = 8 \times 8 = 64 \) bulbs

So the number of dahlia bulbs will be:
- Year 1: 8 bulbs
- Year 2: 16 bulbs
- Year 3: 32 bulbs
- Year 4: 64 bulbs

I hope this helps you with your math test preparation and gives you a better understanding of your friend's gardening situation!