To determine the rule for generating the next term in the sequence 23, 19.5, 16, 12.5..., let's examine the differences between the consecutive terms:
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The difference between the first and second term:
\( 23 - 19.5 = 3.5 \) -
The difference between the second and third term:
\( 19.5 - 16 = 3.5 \) -
The difference between the third and fourth term:
\( 16 - 12.5 = 3.5 \)
We can see that the difference between consecutive terms is consistently \( 3.5 \). This means that the sequence is decreasing by \( 3.5 \) each time.
To find the next term, we can subtract \( 3.5 \) from the last term (\( 12.5 \)): \[ 12.5 - 3.5 = 9 \]
Thus, the next term in the sequence would be \( 9 \).
The rule for generating the next term in the sequence can be stated as: Subtract \( 3.5 \) from the previous term.
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