Question

Given the first two terms of different arithmetic sequences as -9 and -4, what are the next three terms of each sequence? Type the answers in the boxes below.

Answer 1

To find the next three terms of the arithmetic sequences starting with -9 and -4, calculate the common difference and add it to the latest term. The common difference is 5, resulting in the next terms being 1, 6, and 11.

Step-by-step explanation:

The question asks to calculate the next three terms of two arithmetic sequences given the first two terms as -9 and -4. In an arithmetic sequence, each term is equal to the previous term plus a constant difference (d). To find next terms in the sequence, we add the common difference to the last known term.

The common difference (d) is found by subtracting the first term from the second term. In this case:

d = -4 - (-9) = -4 + 9 = 5.

Now, to find the next three terms of the sequence, we add the common difference to the last known term repeatedly:

1. Third term: -4 + 5 = 1
2. Fourth term: 1 + 5 = 6
3. Fifth term: 6 + 5 = 11

So, the next three terms of the arithmetic sequence are 1, 6, and 11.