# SOLUTION: Algebra 2 worksheet on Arithmetic sequence The third term of an arithmetic sequence is 9 and the seventh term is 31. Find the sum of the first twenty-two terms. How many t

Algebra ->  Algebra  -> Sequences-and-series -> SOLUTION: Algebra 2 worksheet on Arithmetic sequence The third term of an arithmetic sequence is 9 and the seventh term is 31. Find the sum of the first twenty-two terms. How many t      Log On

 Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 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 202838: Algebra 2 worksheet on Arithmetic sequence The third term of an arithmetic sequence is 9 and the seventh term is 31. Find the sum of the first twenty-two terms. How many terms of the arithmetic sequence 2,4,6,8, ... add up to 60,762? Answer by Edwin McCravy(8882)   (Show Source): You can put this solution on YOUR website!The third term of an arithmetic sequence is 9 and the seventh term is 31. Find the sum of the first twenty-two terms. ``` ___, ___, 9 , ___, ___, ___, 31, ... The nth term formula is Substitute in Substitute Now Substitute in Substitute So we have the system: Solve the first equation for Substitute in the second equation: Substituting in Now we can use the formula for the sum of the first n terms: Substitute , , ---------------- ``` How many terms of the arithmetic sequence 2,4,6,8, ... add up to 60,762 ``` Subtract any two consecutive terms and get = the first term, which is , and Multiply both sides by 2: Divide through by 2 Factor: or or We discard the negative answer, and so Edwin```