write an explicit formula for each arithmetic sequence. -2,7,16,25
The explicit formula for this arithmetic sequence is:
an = -2 + (n-1)9
where "an" represents the nth term in the sequence.
is that correct
Yes, that's correct!
show your work
Sure, I'd be happy to show my work.
To find the explicit formula for an arithmetic sequence, we can use the formula:
an = a1 + (n-1)d
where "an" represents the nth term in the sequence, "a1" represents the first term, "n" represents the term number we are trying to find, and "d" represents the common difference between terms.
Given the sequence -2, 7, 16, 25, we can see that the common difference between terms is 9. We can also see that the first term (a1) is -2. So, substituting these values into the formula, we get:
an = -2 + (n-1)9
This is the explicit formula for the arithmetic sequence -2, 7, 16, 25.
no words
an = -2 + (n-1)9
show the steps with no words
an = -2 + (n-1)9
an = -2 + 9n - 9
an = 7 + 9n - 9
an = 9n - 2
To find the explicit formula for an arithmetic sequence, we can use the formula:
\[a_n = a_1 + (n-1)d\]
where:
- \(a_n\) is the \(n\)th term in the sequence
- \(a_1\) is the first term in the sequence
- \(d\) is the common difference
In this case, the first term, \(a_1\), is -2, and the common difference, \(d\), is 9.
Substituting these values into the formula, we have:
\[a_n = -2 + (n-1) \cdot 9\]
Simplifying further:
\[a_n = -2 + 9n - 9\]
Combining like terms:
\[a_n = 7n - 11\]
Therefore, the explicit formula for the arithmetic sequence -2, 7, 16, 25 is \(a_n = 7n - 11\).