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Answer and step-by-step explanation:
To find the next term of the sequence, let's find the common difference by subtracting a term by the previous term.
23, 15, 7, -1, …
15 - 23 = -8
7 - 15 = -8
-1 - 7 = -8
Observe that all of their differences are the same and the given sequence is an arithmetic sequence. Thus, the common difference is -8.
Let's use the formula for an arithmetic sequence to find the next term which is the 5th term:
An = A1 + (n-1)d
where
An is the nth term,
A1 is the first term,
n is the number of terms and
d is the common difference.
Let's substitute the given values to the formula. Then simplify.
An = A5
A1 = 23
n = 5
d = -8
A5 = 23 + (5 - 1)(-8)
A5 = 23 + (4)(-8)
A5 = 23 - 32
A5 = -9