Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 641 · 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 the first 9 terms of the AP 2, 4, 6, …? (a) 90 (b) 180 (c) 18 (d) 99
2. 2.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 60 (b) 110 (c) 10 (d) 55
3. 3.What is the sum of the first 10 terms of the AP 9, 13, 17, …? (a) 290 (b) 45 (c) 540 (d) 270
4. 4.What is the missing term in the AP 5, 9, 13, ?, 21? (a) 21 (b) 18 (c) 16 (d) 17
5. 5.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 55 (b) 45 (c) 17 (d) 90
6. 6.What is the sum of all the whole numbers from 1 to 41? (a) 861 (b) 820 (c) 862 (d) 1722
7. 7.What is the 34th term of the AP 2, 4, 6, 8, …? (a) 66 (b) 69 (c) 70 (d) 68
8. 8.Which term of the AP 8, 15, 22, 29, … is 57? (a) 10th (b) 9th (c) 7th (d) 8th
9. 9.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 231 (d) 41
10. 10.What is the 37th term of the AP 17, 22, 27, 32, …? (a) 180 (b) 185 (c) 197 (d) 202
11. 11.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 63 (b) 15 (c) 126 (d) 70
12. 12.What is the 19th term of the AP 13, 15, 17, 19, …? (a) 38 (b) 36 (c) 51 (d) 49
13. 13.Which term of the AP 20, 28, 36, 44, … is 108? (a) 14th (b) 13th (c) 12th (d) 11th
14. 14.What is the 30th term of the AP 16, 18, 20, 22, …? (a) 58 (b) 74 (c) 60 (d) 76
15. 15.What is the 22nd term of the AP 2, 6, 10, 14, …? (a) 90 (b) 86 (c) 88 (d) 84
16. 16.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 138 (b) 240 (c) 120 (d) 35
17. 17.What is the 35th term of the AP 14, 22, 30, 38, …? (a) 280 (b) 272 (c) 286 (d) 294
18. 18.Which term of the AP 7, 10, 13, 16, … is 28? (a) 10th (b) 8th (c) 7th (d) 9th
19. 19.What is the sum of all the whole numbers from 1 to 14? (a) 105 (b) 98 (c) 91 (d) 210
20. 20.Which term of the AP 20, 23, 26, 29, … is 62? (a) 14th (b) 16th (c) 17th (d) 15th
21. 21.What is the 14th term of the AP 18, 26, 34, 42, …? (a) 104 (b) 130 (c) 122 (d) 112
22. 22.Which term of the AP 5, 8, 11, 14, … is 119? (a) 38th (b) 40th (c) 41st (d) 39th
23. 23.What is the missing term in the AP 15, 22, ?, 36, 43? (a) 36 (b) 30 (c) 28 (d) 29
24. 24.What is the 12th term of the AP 1, 6, 11, 16, …? (a) 55 (b) 60 (c) 56 (d) 61
25. 25.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 14 (b) 63 (c) 56 (d) 112
26. 26.What is the sum of the first 9 terms of the AP 5, 7, 9, …? (a) 126 (b) 117 (c) 234 (d) 21
27. 27.What is the 10th term of the AP 16, 24, 32, 40, …? (a) 96 (b) 72 (c) 80 (d) 88
28. 28.Which term of the AP 11, 20, 29, 38, … is 317? (a) 34th (b) 36th (c) 35th (d) 37th
29. 29.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 4 (b) 5 (c) 3 (d) 2
30. 30.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
31. 31.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 40 (b) 216 (c) 234 (d) 432
32. 32.What is the 32nd term of the AP 11, 14, 17, 20, …? (a) 104 (b) 93 (c) 107 (d) 96
33. 33.What is the missing term in the AP 13, ?, 29, 37, 45? (a) 22 (b) 21 (c) 20 (d) 29
34. 34.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 900 (c) 930 (d) 465
35. 35.What is the 21st term of the AP 6, 10, 14, 18, …? (a) 84 (b) 86 (c) 80 (d) 90
36. 36.What is the 10th term of the AP 2, 6, 10, 14, …? (a) 42 (b) 36 (c) 40 (d) 38
37. 37.What is the sum of all the whole numbers from 1 to 13? (a) 92 (b) 91 (c) 78 (d) 182
38. 38.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 338 (c) 702 (d) 351
39. 39.What is the 20th term of the AP 8, 12, 16, 20, …? (a) 84 (b) 76 (c) 80 (d) 88
40. 40.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 578 (c) 595 (d) 1190

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