An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This means that each term is obtained by adding or subtracting the same number from the previous term. For example, in the sequence 2, 5, 8, 11, 14, the difference between consecutive terms is 3.
An arithmetic sequence can be identified in a word problem by looking for a pattern where the difference between consecutive terms is constant. The problem may also explicitly state that the sequence is arithmetic.
The common difference in an arithmetic sequence can be found by subtracting any two consecutive terms. This will give you the constant value that is added or subtracted to get from one term to the next.
To find a specific term in an arithmetic sequence, you can use the formula an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference. Simply plug in the values given in the problem to find the desired term.
Yes, an arithmetic sequence can have negative terms. As long as the difference between consecutive terms is constant, the sequence can include both positive and negative numbers.