Question

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**.