Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 361 · 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 missing term in the AP 12, ?, 16, 18, 20? (a) 14 (b) 16 (c) 13 (d) 15
2. 2.What is the 24th term of the AP 9, 13, 17, 21, …? (a) 105 (b) 96 (c) 101 (d) 92
3. 3.What is the sum of all the whole numbers from 1 to 41? (a) 862 (b) 820 (c) 1722 (d) 861
4. 4.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 252 (b) 504 (c) 32 (d) 264
5. 5.What is the 29th term of the AP 2, 11, 20, 29, …? (a) 261 (b) 254 (c) 252 (d) 263
6. 6.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 15 (b) 48 (c) 90 (d) 45
7. 7.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 342 (c) 35 (d) 171
8. 8.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 25 (d) 169
9. 9.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 50 (b) 26 (c) 25 (d) 7
10. 10.What is the 32nd term of the AP 5, 11, 17, 23, …? (a) 186 (b) 192 (c) 191 (d) 197
11. 11.What is the 18th term of the AP 6, 13, 20, 27, …? (a) 132 (b) 119 (c) 125 (d) 126
12. 12.Which term of the AP 11, 18, 25, 32, … is 81? (a) 12th (b) 13th (c) 11th (d) 10th
13. 13.What is the sum of all the whole numbers from 1 to 61? (a) 3782 (b) 1891 (c) 1892 (d) 1830
14. 14.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 200 (b) 112 (c) 23 (d) 100
15. 15.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 280 (b) 46 (c) 300 (d) 560
16. 16.What is the 14th term of the AP 16, 20, 24, 28, …? (a) 72 (b) 56 (c) 68 (d) 52
17. 17.What is the 25th term of the AP 18, 25, 32, 39, …? (a) 186 (b) 168 (c) 193 (d) 175
18. 18.What is the sum of all the whole numbers from 1 to 95? (a) 4561 (b) 9120 (c) 4465 (d) 4560
19. 19.What is the 32nd term of the AP 6, 9, 12, 15, …? (a) 96 (b) 99 (c) 102 (d) 93
20. 20.What is the 29th term of the AP 17, 22, 27, 32, …? (a) 140 (b) 145 (c) 162 (d) 157
21. 21.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 30 (b) 50 (c) 9 (d) 25
22. 22.What is the missing term in the AP 7, 13, 19, ?, 31? (a) 26 (b) 25 (c) 24 (d) 31
23. 23.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 253 (c) 506 (d) 43
24. 24.What is the 14th term of the AP 5, 14, 23, 32, …? (a) 126 (b) 117 (c) 131 (d) 122
25. 25.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 10 (b) 15 (c) 12 (d) 11
26. 26.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 650 (c) 300 (d) 325
27. 27.What is the 16th term of the AP 2, 5, 8, 11, …? (a) 50 (b) 45 (c) 48 (d) 47
28. 28.What is the 34th term of the AP 3, 7, 11, 15, …? (a) 136 (b) 139 (c) 135 (d) 132
29. 29.What is the 38th term of the AP 4, 7, 10, 13, …? (a) 114 (b) 111 (c) 118 (d) 115
30. 30.What is the sum of the first 11 terms of the AP 5, 8, 11, …? (a) 223 (b) 35 (c) 440 (d) 220
31. 31.What is the 21st term of the AP 3, 12, 21, 30, …? (a) 189 (b) 180 (c) 183 (d) 192
32. 32.What is the missing term in the AP 15, 22, 29, ?, 43? (a) 36 (b) 35 (c) 37 (d) 43
33. 33.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 180 (b) 20 (c) 174 (d) 348
34. 34.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 42 (b) 196 (c) 216 (d) 392
35. 35.What is the 14th term of the AP 12, 17, 22, 27, …? (a) 65 (b) 82 (c) 70 (d) 77
36. 36.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 28 (c) 49 (d) 13
37. 37.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 722 (c) 1482 (d) 741
38. 38.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 432 (b) 221 (c) 216 (d) 44
39. 39.What is the missing term in the AP 1, 4, 7, ?, 13? (a) 10 (b) 11 (c) 9 (d) 13
40. 40.What is the 23rd term of the AP 2, 5, 8, 11, …? (a) 69 (b) 66 (c) 68 (d) 71

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