finish the arithmetic sequence 24,__,__,-3

Answer 1

To find the missing numbers in the arithmetic sequence 24, __, __, -3, we first need to identify the common difference.

1. The first term is 24 and the last term is -3. The number of terms in the sequence is 4 (24, _, _, -3).
2. We can denote the common difference as \(d\).
3. In an arithmetic sequence, the last term can be expressed as follows:

\[ \text{Last Term} = \text{First Term} + (n-1)d \]

Here, \(n\) is the number of terms. For this sequence:

\[ -3 = 24 + (4-1)d \] \[ -3 = 24 + 3d \] \[ -3 - 24 = 3d \] \[ -27 = 3d \] \[ d = -9 \]

4. Now that we have found the common difference \(d = -9\), we can find the missing terms:

• The second term: \[ 24 + (-9) = 15 \]

• The third term: \[ 15 + (-9) = 6 \]

Thus, the completed arithmetic sequence is 24, 15, 6, -3.