ARITHMETIC SEQUENCE AND SERIES
Formulas:
Find the last term (un).1. u1 = 7 d = 8 n = 60
2. u1 = -5 d = 6 n = 51
3. u1 = 4 d = -3 n = 77
4. Find the 18th term of the sequence
8, 11, 14, …
5. Find the 50th term of the sequence
8, 5, 2, …
6. Find the 100th term of the sequence
-3, 2, 7, …
Find the arithmetic mean (average) of the terms in each sequence.
7. 3, __, __, __, __, 33
8. –2, __, __, __, __, __, 40
9. 11, __, __, __, -13
Find the number of terms in the sequence.
10. 18, 24, 30, …, 618
11. 71, 65, 59, …, –43
12. –2,5,12, …, 222 / Find the sum.
13. u1 = 4 u50 = 254 n = 50
14. u1 = -10 u83 = 115 n = 100
15. 2, 7, 12, …, u55
16. 8, -1, -10, …, -100
17. –20, -14, -8, …, 250
18. The front row of a theater has 10 seats. Each of the other rows has two more seats than the row before it. How many seats are there in the 23rd row?
19. If Aunt Millie sent you $100 on your first birthday, and then increased each successive birthday present by $10, how much will you receive on your twenty-first birthday?
20. Every hour a cuckoo clock sounds as many times as the hour. How many times does it sound starting with the first sound at 1 P.M. and continuing on through the last sound at midnight?
21. Sarah gets a starting salary of $14,600 and annual raises of $700. How much money did she make in her first 10 years?
GEOMETRIC SEQUENCES AND SERIES
Formulas:
Find the last term (un)1. u1 = 3 r = 5 n = 6
2. u1 = -2 r = 6 n = 8
3. u1 = 7 r = -2 n = 7
4. u1 = 7 r = -2 n = 8
5. Find the 10th term of the sequence
2, 6, 18, …
6. Find the 8th term of the sequence
-5, 10, -20, …
7. Find the 9th term of the sequence
12, 3, , …
Find the “geometric mean” of the terms in each sequence. (HINT: Google it.)
8. 3, ____, ____, ____, 48
9. –2, ___, ___, ___, ___, -486
10. 5, ___, ___, 135
Find the number of terms in the sequence.
11. 3, 6, 12, …, 192
12. 2, 6, 18, …, 486
13. 5, -10, 20, …, 320 / Find the sum.
14. u1 = 3 r = 2 n = 7
15. u1 = 7 r = -3 n = 6
16. u1 = 5 r = n = 6
17. 3, 6, 12, …, 6144
18. 128, 192, 288, …, 1458
SOLVE EACH
19. If you save $0.05 on the first day and double it each day thereafter, how much money will you have saved on day 20?
20. Andrea received a 5% salary increase at the end of each of 8 years. If her starting salary was $8000, how much did she earn in all during the 8 years?
21. A real estate agent is selling a house for $100,000. She is telling a prospective buyer that the house will increase in value by 10% each year. What will be the cost of house in 5 years?
22. Joan is saving some dimes each day. She saves 1 dime the 1st day, 2 dimes the 2nd day, 3 dimes the 3rd day, and so on. How much money will she have at the end of 30 days?
23. Cans are stacked in 20 rows with 1 can in the top row, 2 in the next row below, 3 in the next row below, and so on. How many cans are in the stack?