Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Find the sum of each finite arithmetic series.

8. 2 + 4 + 6 + 8 2 plus 4 plus 6 plus 8
9. 8 + 9 + 10 + ⋯ + 15 8 plus 9 plus 10 plus math axis ellipsis plus 15
10. 5 + 6 + 7 + ⋯ + 11 5 plus 6 plus 7 plus math axis ellipsis plus 11
11. 1 + 4 + 7 + ⋯ + 31 1 plus 4 plus 7 plus math axis ellipsis plus 31
12. 7 + 14 + 21 + ⋯ + 105 7 plus 14 plus 21 plus math axis ellipsis plus 105
13. ( − 3 ) + ( − 6 ) + ( − 9 ) + ⋯ + ( − 30 ) open negative 3 close , plus , open negative 6 close , plus , open negative 9 close , plus math axis ellipsis plus . open negative 30 close

See Problem 2.

14. Grades A student has taken three math tests so far this semester. His scores for the first three tests were 75, 79, and 83.
    1. Suppose his test scores continue to improve at the same rate. What will be his grade on the sixth (and final) test?
    2. What will be his total score for all six tests?

See Problem 3.

Write each arithmetic series in summation notation.

15. 4 + 8 + 12 + 16 + 20 4 plus 8 plus 12 plus 16 plus 20
16. 7 + 9 + 11 + ⋯ + 21 7 plus 9 plus 11 plus math axis ellipsis plus 21
17. 5 + 8 + 11 + ⋯ + 38 5 plus 8 plus 11 plus math axis ellipsis plus 38
18. 100 + 90 + 80 + ⋯ + 10 100 plus 90 plus 80 plus math axis ellipsis plus 10
19. ( − 3 ) + ( − 6 ) + ( − 9 ) + ⋯ + ( − 30 ) open negative 3 close , plus , open negative 6 close , plus , open negative 9 close , plus math axis ellipsis plus . open negative 30 close
20. 105 + 97 + 89 + ⋯ + ( − 71 ) 105 plus 97 plus 89 plus math axis ellipsis plus . open negative 71 close

See Problem 4.

Find the sum of each finite series.

21. ∑ n = 1 5 ( 2 n − 1 ) sum , from , n equals 1 , to , 5 , of . open , 2 n minus 1 , close
22. ∑ n = 1 10 ( 3 n − 4 ) sum , from , n equals 1 , to , 10 , of . open , 3 n minus 4 , close
23. ∑ n = 1 8 ( 7 − n ) sum , from , n equals 1 , to , 8 , of . open , 7 minus n , close
24. ∑ n = 1 4 2 n sum , from , n equals 1 , to , 4 , of . 2 to the n
25. ∑ n = 1 9 ( − 1 ) n ⋅ 2 sum , from , n equals 1 , to , 9 , of . open , negative 1 , close to the n . dot 2
26. ∑ n = 5 10 ( 20 − n ) sum , from , n equals 5 , to , 10 , of . open , 20 minus n , close

See Problem 5.

Use a graphing calculator to find the sum of each series.

27. ∑ n = 1 50 ( 2 n − 3 ) sum , from , n equals 1 , to , 50 , of . open , 2 n minus 3 , close
28. ∑ n = 1 26 ( n 2 − 3 n ) sum , from , n equals 1 , to , 26 , of . open . n squared , minus 3 n . close
29. ∑ n = 1 10 ( − 2 ) n sum , from , n equals 1 , to , 10 , of . open , negative 2 , close to the n
30. ∑ n = 1 20 ( n 3 − 10 n 2 ) sum , from , n equals 1 , to , 20 , of . open . n cubed , minus 10 , n squared . close
31. ∑ n = 5 73 ( − 4 n + 32 ) sum , from , n equals 5 , to , 73 , of . open . negative 4 n plus 32 . close
32. ∑ n = 5 25 ( n 2 − 14 n + 32 ) sum , from , n equals 5 , to , 25 , of . open . n squared , minus 14 n plus 32 . close

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