# SOLUTION: Write the next term in the sequence. Then write a rule for the nth term. -5, 10, -15, 20,...

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 Algebra: Sequences of numbers, series and how to sum them Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Sequences-and-series Question 190402: Write the next term in the sequence. Then write a rule for the nth term. -5, 10, -15, 20,...Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!Write the next term in the sequence. Then write a rule for the nth term. -5, 10, -15, 20, ... ``` If it weren't for the signs, we would have the sequence 5, 10, 15, 20, ... So let's first get the nth term of that sequence. The difference between any term and the preceding term is 5. So the common difference d = 5. The nth term of an arithmetic sequence is given by: and Substituting, Now we have to tack on a factor that will cause the signs to alternate: The alternating sign factors are and , depending on whether the first term is negative or positive. Since the first term is -5, a negative number, we use for the alternating sign factor. So if we use (capital "A") for the nth term, we just multiply the nth term for (small "a") above by and get Edwin```