The first 5 terms of an arithmetic sequence are
-2, 5, 12, 19, 26
Find the formula for the nth term of this sequence
keep adding 7, right?
now just recall your formula for an AP if you know a and d.
To find the formula for the nth term of an arithmetic sequence, we need to identify the common difference (d) first. The common difference is the constant value that is added to each term to get the next term.
We can see that the common difference between consecutive terms in this sequence is 7. For example, -2 + 7 = 5, 5 + 7 = 12, and so on.
Now, to find the formula for the nth term, we can use the general formula for arithmetic sequences:
nth term = first term + (n - 1) * common difference
Let's substitute the known values into the formula:
nth term = -2 + (n - 1) * 7
Simplifying further:
nth term = -2 + 7n - 7
nth term = 7n - 9
Therefore, the formula for the nth term of this arithmetic sequence is 7n - 9.
To find the formula for the nth term of an arithmetic sequence, we can use the formula:
nth term = first term + (n - 1) * common difference
In this case, we have the first term (-2) and the common difference (7).
Substituting these values into the formula, we get:
nth term = -2 + (n - 1) * 7
Simplifying further, we have the formula for the nth term of the sequence as:
nth term = -2 + 7n - 7
Combining like terms, the final formula for the nth term of the sequence is:
nth term = 7n - 9