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What is the common difference between the elements of the arithmetic sequence below?

[tex]\[ -18, -22.5, -27, -31.5, -36 \][/tex]

[tex]\[\square\][/tex]


Sagot :

To determine the common difference of an arithmetic sequence, we need to find the difference between successive terms.

Let's look at the given sequence:
[tex]\[ -18, -22.5, -27, -31.5, -36 \][/tex]

By definition, the common difference [tex]\( d \)[/tex] in an arithmetic sequence is the difference between any two consecutive terms. We'll find this difference by subtracting the first term from the second term:

[tex]\[ d = -22.5 - (-18) \][/tex]

Solving inside the parentheses first:
[tex]\[ -22.5 - (-18) = -22.5 + 18 \][/tex]

Carrying out the subtraction:
[tex]\[ -22.5 + 18 = -4.5 \][/tex]

So, the common difference between the elements of the sequence is:
[tex]\[ \boxed{-4.5} \][/tex]

To verify, let's check the difference between another pair of successive terms:

Between the second and third terms:
[tex]\[ d = -27 - (-22.5) = -27 + 22.5 = -4.5 \][/tex]

Between the third and fourth terms:
[tex]\[ d = -31.5 - (-27) = -31.5 + 27 = -4.5 \][/tex]

Between the fourth and fifth terms:
[tex]\[ d = -36 - (-31.5) = -36 + 31.5 = -4.5 \][/tex]

Since the difference is consistent, our common difference is confirmed to be:
[tex]\[ \boxed{-4.5} \][/tex]