## 2 arithmetic sequences and series find the indicated term of each arithmetic sequence. 1. find the sixtieth term of the arithmetic sequence

Question

2 arithmetic sequences and series find the indicated term of each arithmetic sequence. 1. find the sixtieth term of the arithmetic sequence if a1 = 418 and d = 12. 2. find a23 in the sequence, -18, -34, -50, -66, …. write an equation for the nth term of each arithmetic sequence. 3. 45, 30, 15, 0, … 4. -87, -73, -59, -45, … find the sum of each arithmetic series. 5. 5 + 7 + 9 + 11 + … + 27 6. -4 + 1 + 6 + 11 + … + 91 7. 13 + 20 + 27 + … + 272 8. 89 + 86 + 83 + 80 + … + 20 9. ∑ (1 − 2n) 4 n=1 10. ∑ (5 + 3j) 6 j=1 11. ∑ (9 − 4n) 5 n=1 12. ∑ (2k + 1) 10 k=4 13. ∑ (5n − 10) 8 n=3 14. ∑ (4 − 4n) 101 n=1 find the first three terms of each arithmetic series described. 15. a1 = 14, an = -85, sn = -1207 16. a1 = 1, an = 19, sn = 100 17. n = 16, an = 15, sn = -120 18. n = 15, an = 54 5 , sn = 45 name _____________________________________________ date_____________________________ period _____________ 19. stacking a health club rolls its towels and stacks them in layers on a shelf. each layer of towels has one less towel than the layer below it. if there are 20 towels on the bottom layer and one towel on the top layer, how many towels are stacked on the shelf? 20. windows a side of an apartment building is shaped like a steep staircase. the windows are arranged in columns. the first column has 2 windows, the next has 4, then 6, and so on. how many windows are on the side of the apartment building if it has 15 columns? 21. training more than 380,000 people run in u.s. marathons each year. matthew is training to run a marathon. he runs 20 miles his first week of training. each week, he increases the number of miles he runs by 4 miles. how many total miles did he run in 8 weeks of training?

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1. I have the first 8 answers for you:
1: 1126
2: -370
3:[tex]a_n=45-15(n-1)[/tex]
4:[tex]a_n=-87+14(n-1)[/tex]
5: 192
6: 870
7: 5414
8: 1308

The formula for #1 would be [tex]a_n=418+12(n-1)[/tex]. Using 60 for n, we have
418+12(60-1) = 1126

The formula for #2 would be[tex]a_n=-18-16(n-1)[/tex]. Using 23 for n, we have
-18-16(23-1) = -370

The general form for this sequence is[tex]a_n=a_1+d(n-1)[/tex], where au2081 is the first term and d is the common difference. For #3, the first term is 45 and the common difference is -15. For #4, the first term is -87 and the common difference is 14.

For #5-8, add together the terms.

I have the first 8 answers for you:n

1: 1126n

2: -370n

3: n

4: n

5: 192n

6: 870n

7: 5414n

8: 1308n

n

The formula for #1 would be . Using 60 for n, we haven

418+12(60-1) = 1126n

n

The formula for #2 would be . Using 23 for n, we haven

-18-16(23-1) = -370n

n

The general form for this sequence is , where au2081 is the first term and d is the common difference. For #3, the first term is 45 and the common difference is -15. For #4, the first term is -87 and the common difference is 14.n

n

For #5-8, add together the terms.

Step-by-step explanation: