To determine the common difference in the given arithmetic sequence, it is essential to recognize how arithmetic sequences function. In an arithmetic sequence, the difference between consecutive terms remains constant. This fixed difference is called the "common difference."
Given the sequence:
[tex]\[ -18, -22.5, -27, -31.5, -36 \][/tex]
To find the common difference, we can follow these steps:
1. Identify two consecutive terms:
- We can start by selecting the first and second terms in the sequence: [tex]\( -18 \)[/tex] and [tex]\( -22.5 \)[/tex].
2. Subtract the first term from the second term:
[tex]\[ -22.5 - (-18) \][/tex]
3. Simplify the subtraction:
- Note that subtracting a negative number is equivalent to adding its positive counterpart:
[tex]\[ -22.5 + 18 \][/tex]
4. Perform the addition:
[tex]\[ -22.5 + 18 = -4.5 \][/tex]
Thus, the common difference is:
[tex]\[ \boxed{-4.5} \][/tex]
To verify the consistency of the common difference throughout the sequence, we can repeat the subtraction for other pairs of consecutive terms:
1. Second term and third term:
[tex]\[ -27 - (-22.5) = -27 + 22.5 = -4.5 \][/tex]
2. Third term and fourth term:
[tex]\[ -31.5 - (-27) = -31.5 + 27 = -4.5 \][/tex]
3. Fourth term and fifth term:
[tex]\[ -36 - (-31.5) = -36 + 31.5 = -4.5 \][/tex]
Since the common difference remains constant at [tex]\( -4.5 \)[/tex] throughout, we confirm that the sequence's common difference is indeed:
[tex]\[ \boxed{-4.5} \][/tex]
