Write a rule for the nth term of the arithmetic sequence.
-12, -5, 2, 9
the common difference is 7
7 n - 19
To find the rule for the nth term of an arithmetic sequence, we need to determine the common difference between consecutive terms. In this sequence, the common difference is 7 since each term is obtained by adding 7 to the previous term.
The first term of the sequence is -12. To get the second term, we add the common difference of 7 to the first term: -12 + 7 = -5. We can continue this pattern to find the third and fourth terms:
Third term: -5 + 7 = 2
Fourth term: 2 + 7 = 9
So, the rule for the nth term of this arithmetic sequence is:
nth term = -12 + (n - 1) * 7
To find the rule for the nth term of an arithmetic sequence, you need to determine the common difference between consecutive terms. In this sequence, we can see that each term is obtained by adding 7 to the previous term.
Therefore, the rule for the nth term of this arithmetic sequence is:
nth term = -12 + (n-1) * 7
To explain how this rule is derived, you can start by identifying the first term of the sequence, which is -12. Then, you observe that to reach the second term, you add 7 to the first term: -12 + 7 = -5. This pattern continues for the subsequent terms as well.
To generalize this pattern, we note that the difference between any two terms in an arithmetic sequence is always the same. In this case, it is 7. So, to get from the first term to the nth term, we add (n-1) lots of 7, where n represents the position of the term in the sequence. Adding (n-1) * 7 to the first term yields the formula for the nth term.