Questions: The first three terms of an arithmetic sequence are as follows. -19, -14, -9 Find the next two terms of this sequence. -19, -14, -9,

Solution Steps

To find the next two terms of an arithmetic sequence, we need to determine the common difference between consecutive terms. Once we have the common difference, we can add it to the last known term to find the next term, and repeat this process to find the subsequent term.

1. Calculate the common difference by subtracting the first term from the second term.
2. Add the common difference to the last known term to find the next term.
3. Repeat the process to find the subsequent term.

The first three terms of the arithmetic sequence are given as \( -19, -14, -9 \). To find the common difference \( d \), we calculate: \[ d = -14 - (-19) = 5 \]

Using the common difference, we find the next term in the sequence: \[ \text{Next term}_1 = -9 + d = -9 + 5 = -4 \]

We continue to find the next term after the first new term: \[ \text{Next term}_2 = -4 + d = -4 + 5 = 1 \]

Final Answer