Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 596 · 40 questions

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

1. 1.What is the 28th term of the AP 12, 17, 22, 27, …? (a) 147 (b) 152 (c) 140 (d) 135
2. 2.What is the 39th term of the AP 7, 11, 15, 19, …? (a) 163 (b) 156 (c) 159 (d) 152
3. 3.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 10 (b) 6 (c) 5 (d) 7
4. 4.What is the 39th term of the AP 5, 12, 19, 26, …? (a) 273 (b) 266 (c) 278 (d) 271
5. 5.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 35 (b) 36 (c) 70 (d) 9
6. 6.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 66 (c) 132 (d) 21
7. 7.What is the missing term in the AP 1, ?, 15, 22, 29? (a) 8 (b) 15 (c) 7 (d) 9
8. 8.What is the 33rd term of the AP 1, 10, 19, 28, …? (a) 298 (b) 288 (c) 297 (d) 289
9. 9.What is the missing term in the AP 1, 6, ?, 16, 21? (a) 12 (b) 16 (c) 11 (d) 10
10. 10.What is the 31st term of the AP 2, 10, 18, 26, …? (a) 240 (b) 250 (c) 248 (d) 242
11. 11.What is the sum of all the whole numbers from 1 to 77? (a) 3004 (b) 3003 (c) 2926 (d) 6006
12. 12.What is the 24th term of the AP 3, 9, 15, 21, …? (a) 144 (b) 141 (c) 147 (d) 138
13. 13.What is the 39th term of the AP 13, 15, 17, 19, …? (a) 91 (b) 78 (c) 89 (d) 76
14. 14.What is the missing term in the AP 14, 19, 24, ?, 34? (a) 34 (b) 29 (c) 30 (d) 28
15. 15.What is the 40th term of the AP 20, 23, 26, 29, …? (a) 120 (b) 140 (c) 117 (d) 137
16. 16.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 14 (b) 43 (c) 80 (d) 40
17. 17.What is the missing term in the AP 20, ?, 32, 38, 44? (a) 26 (b) 25 (c) 27 (d) 32
18. 18.What is the 17th term of the AP 9, 15, 21, 27, …? (a) 105 (b) 102 (c) 111 (d) 96
19. 19.What is the missing term in the AP 7, ?, 13, 16, 19? (a) 9 (b) 13 (c) 10 (d) 11
20. 20.What is the 21st term of the AP 4, 8, 12, 16, …? (a) 80 (b) 85 (c) 88 (d) 84
21. 21.Which term of the AP 3, 8, 13, 18, … is 173? (a) 36th (b) 34th (c) 35th (d) 37th
22. 22.What is the 30th term of the AP 10, 15, 20, 25, …? (a) 160 (b) 145 (c) 155 (d) 150
23. 23.What is the 13th term of the AP 15, 23, 31, 39, …? (a) 104 (b) 119 (c) 111 (d) 96
24. 24.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 84 (b) 24 (c) 168 (d) 96
25. 25.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
26. 26.What is the missing term in the AP 4, 13, ?, 31, 40? (a) 23 (b) 31 (c) 22 (d) 21
27. 27.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 41 (c) 462 (d) 441
28. 28.Which term of the AP 11, 14, 17, 20, … is 32? (a) 7th (b) 10th (c) 9th (d) 8th
29. 29.What is the 32nd term of the AP 4, 6, 8, 10, …? (a) 62 (b) 68 (c) 64 (d) 66
30. 30.What is the 15th term of the AP 10, 18, 26, 34, …? (a) 120 (b) 112 (c) 130 (d) 122
31. 31.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 132 (b) 228 (c) 114 (d) 34
32. 32.Which term of the AP 10, 17, 24, 31, … is 269? (a) 39th (b) 38th (c) 37th (d) 40th
33. 33.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 95 (b) 14 (c) 100 (d) 190
34. 34.What is the missing term in the AP 13, 16, ?, 22, 25? (a) 20 (b) 22 (c) 19 (d) 18
35. 35.What is the missing term in the AP 13, 17, ?, 25, 29? (a) 25 (b) 20 (c) 22 (d) 21
36. 36.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 45 (c) 110 (d) 50
37. 37.What is the 13th term of the AP 15, 21, 27, 33, …? (a) 78 (b) 72 (c) 93 (d) 87
38. 38.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 22 (b) 19 (c) 17 (d) 18
39. 39.What is the 12th term of the AP 4, 13, 22, 31, …? (a) 99 (b) 108 (c) 112 (d) 103
40. 40.What is the 24th term of the AP 1, 10, 19, 28, …? (a) 216 (b) 207 (c) 217 (d) 208

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