The explicit formula for the sequence -5, -3, -1, 1, 3 is a_n = -5 + (n - 1)2.
What is an arithmetic sequence?
Each term of an arithmetic sequence can be found using the formula:
a_n = a + (n-1)d
- Where a is the first term,
- n is the position of the term,
- a_n is the nth term of the sequence,
- d is the common difference of the sequence.
We can find the explicit formula for this sequence as follows:
The given sequence is 5, -3, -1, 1, 3.
From this, we can see that the value of:
a = -5
d = -3 - (-5) = -3 + 5 = 2
∴ The explicit formula can be written as:
a_n = -5 + (n - 1)2
Therefore we have found the explicit formula for the sequence -5, -3, -1, 1, 3 as a_n = -5 + (n - 1)2.
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