Grade 11 · Practice problems
Arithmetic sequences
50 problems, including 17 🔥 challenging (exam-level, multi-step). Work through them on paper, then reveal every answer to check.
1. Find the common difference of 5, 8, 11, 14, \dots
2. Find the common difference of 20, 17, 14, \dots
3. Write the next two terms of 3, 7, 11, \dots
4. State t_1 and d for 9, 14, 19, \dots
5. For t_1 = 4, d = 3, find t_5.
6. For t_1 = 10, d = -2, find t_6.
7. Find the common difference of -4, -1, 2, 5, \dots
8. Is 2, 4, 8, 16 an arithmetic sequence? Explain.
9. For t_1 = 7, d = 0.5, find t_3.
10. Find the common difference of 100, 92, 84, \dots
11. Find t_{20} of 2, 5, 8, \dots
12. Find a formula for t_n of 6, 10, 14, \dots
13. Find t_{15} of 50, 46, 42, \dots
14. Given t_3 = 11 and t_7 = 27, find d.
15. For that sequence, find t_1.
16. Given t_5 = 20 and t_9 = 36, find t_1 and d.
17. Is 100 a term of 4, 9, 14, \dots? Which term?
18. Is 96 a term of 6, 9, 12, \dots? Which term?
19. Find n if t_n = 45 in 3, 5, 7, \dots
20. The first term is 8 and the 12th term is 41. Find d.
21. Which term of 2, 6, 10, \dots equals 202?
22. A theatre has 22 seats in row 1 and 4 more in each next row. Seats in row 18?
23. A log stack has 30 logs in the bottom row and 2 fewer in each row up. Logs in row 10?
24. You save $50 the first week and $15 more each week. Total added in week 8?
25. Find t_n for 100, 97, 94, \dots and use it to find t_{25}.
26. The 4th term is 19 and the 10th is 43. Find the first three terms.
27. A car worth $26000 loses $1500 each year. Its value after 6 years (the 7th yearly value)?
28. Find t_{30} of -5, -2, 1, 4, \dots
29. In an arithmetic sequence t_6 = 17 and d = 3. Find t_1.
30. Air cools 2.5^\circC per 1000 m of altitude; the ground is 20^\circC. Temperature at 5000 m?
31. Find t_1 if t_8 = 50 and t_{15} = 99.
32. How many terms are in 5, 8, 11, \dots, 50?
33. Find t_{12} of 1, 4, 7, 10, \dots
34. 🔥 ChallengingThe 5th term is three times the 2nd term and the 8th term is 30. Find t_1 and d.
35. 🔥 ChallengingInsert three arithmetic means between 5 and 21.
36. 🔥 ChallengingInsert four arithmetic means between 3 and 33.
37. 🔥 ChallengingThe arithmetic mean of two numbers is 17 and one number is 12. Find the other.
38. 🔥 ChallengingThree consecutive arithmetic terms have middle term 8 and common difference 5. Find them.
39. 🔥 ChallengingIn an arithmetic sequence t_3 = 7 and t_8 = 22. Which term equals 40?
40. 🔥 ChallengingIn an arithmetic sequence t_2 + t_4 = 20 and t_6 = 22. Find t_1 and d.
41. 🔥 ChallengingAn arithmetic sequence has t_1 = x and d = x. Its 4th term is 20. Find x.
42. 🔥 ChallengingThe 10th term of an arithmetic sequence exceeds the 4th term by 18. Find d.
43. 🔥 ChallengingAn arithmetic sequence has t_n = 2n + 5. Find t_1, d, and t_{100}.
44. 🔥 ChallengingFor 4, 11, 18, \dots, between which two consecutive terms does 100 fall?
45. 🔥 ChallengingA brick pile's top row has b bricks and each lower row has 3 more; the 9th row down has 40. Find b.
46. 🔥 ChallengingA polygon's interior angles are arithmetic: smallest 100^\circ, common difference 10^\circ, largest 160^\circ. How many sides?
47. 🔥 ChallengingIn an arithmetic sequence the pth term is q and the qth term is p (with p \ne q). Find the (p+q)th term.
48. 🔥 ChallengingAn arithmetic sequence has 20 terms; its first term is 4 and its last term is 61. Find d.
49. 🔥 ChallengingA salary starts at $42000 and rises $1800 each year. In which year does it first exceed $60000?
50. 🔥 ChallengingFind three numbers in arithmetic sequence with sum 15 and product 105.