Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 429 · 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 sum of all the whole numbers from 1 to 26? (a) 325 (b) 702 (c) 338 (d) 351
2. 2.What is the 12th term of the AP 13, 20, 27, 34, …? (a) 97 (b) 90 (c) 77 (d) 84
3. 3.What is the 29th term of the AP 1, 6, 11, 16, …? (a) 140 (b) 145 (c) 146 (d) 141
4. 4.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 1953 (c) 2017 (d) 2016
5. 5.What is the 29th term of the AP 9, 11, 13, 15, …? (a) 58 (b) 67 (c) 56 (d) 65
6. 6.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 396 (b) 201 (c) 198 (d) 33
7. 7.What is the 20th term of the AP 9, 13, 17, 21, …? (a) 89 (b) 80 (c) 76 (d) 85
8. 8.Which term of the AP 12, 16, 20, 24, … is 48? (a) 11th (b) 12th (c) 9th (d) 10th
9. 9.Which term of the AP 10, 13, 16, 19, … is 52? (a) 14th (b) 17th (c) 16th (d) 15th
10. 10.Which term of the AP 10, 17, 24, 31, … is 276? (a) 40th (b) 41st (c) 38th (d) 39th
11. 11.What is the 27th term of the AP 18, 21, 24, 27, …? (a) 78 (b) 99 (c) 96 (d) 81
12. 12.Which term of the AP 20, 27, 34, 41, … is 265? (a) 37th (b) 38th (c) 35th (d) 36th
13. 13.What is the 40th term of the AP 8, 16, 24, 32, …? (a) 312 (b) 321 (c) 328 (d) 320
14. 14.What is the 27th term of the AP 2, 11, 20, 29, …? (a) 245 (b) 236 (c) 234 (d) 243
15. 15.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 110 (d) 55
16. 16.What is the sum of all the whole numbers from 1 to 57? (a) 3306 (b) 1654 (c) 1653 (d) 1596
17. 17.Which term of the AP 17, 23, 29, 35, … is 119? (a) 18th (b) 17th (c) 20th (d) 19th
18. 18.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 804 (b) 61 (c) 432 (d) 402
19. 19.What is the 24th term of the AP 4, 9, 14, 19, …? (a) 119 (b) 124 (c) 120 (d) 115
20. 20.What is the missing term in the AP 6, 8, 10, ?, 14? (a) 13 (b) 12 (c) 11 (d) 14
21. 21.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 88 (b) 9 (c) 48 (d) 44
22. 22.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 81 (d) 17
23. 23.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 32 (b) 187 (c) 190 (d) 374
24. 24.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 44 (b) 184 (c) 208 (d) 368
25. 25.What is the missing term in the AP 7, ?, 15, 19, 23? (a) 10 (b) 12 (c) 15 (d) 11
26. 26.What is the missing term in the AP 18, 22, 26, ?, 34? (a) 34 (b) 31 (c) 29 (d) 30
27. 27.What is the 28th term of the AP 11, 14, 17, 20, …? (a) 95 (b) 92 (c) 84 (d) 81
28. 28.What is the 17th term of the AP 2, 4, 6, 8, …? (a) 35 (b) 34 (c) 36 (d) 32
29. 29.What is the 31st term of the AP 18, 21, 24, 27, …? (a) 111 (b) 108 (c) 90 (d) 93
30. 30.What is the 30th term of the AP 12, 15, 18, 21, …? (a) 90 (b) 102 (c) 87 (d) 99
31. 31.Which term of the AP 6, 9, 12, 15, … is 42? (a) 14th (b) 15th (c) 12th (d) 13th
32. 32.What is the missing term in the AP 16, 23, 30, ?, 44? (a) 37 (b) 36 (c) 44 (d) 38
33. 33.Which term of the AP 12, 17, 22, 27, … is 122? (a) 24th (b) 25th (c) 22nd (d) 23rd
34. 34.What is the 32nd term of the AP 11, 13, 15, 17, …? (a) 62 (b) 75 (c) 64 (d) 73
35. 35.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 120 (c) 240 (d) 225
36. 36.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 230 (b) 225 (c) 450 (d) 45
37. 37.What is the missing term in the AP 7, 16, 25, ?, 43? (a) 33 (b) 35 (c) 34 (d) 43
38. 38.What is the 34th term of the AP 19, 22, 25, 28, …? (a) 121 (b) 99 (c) 118 (d) 102
39. 39.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 31 (b) 192 (c) 96 (d) 114
40. 40.What is the 39th term of the AP 11, 13, 15, 17, …? (a) 76 (b) 87 (c) 89 (d) 78

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