Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 69 · 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.Which term of the AP 1, 5, 9, 13, … is 81? (a) 20th (b) 21st (c) 23rd (d) 22nd
2. 2.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 42 (b) 198 (c) 203 (d) 396
3. 3.What is the 26th term of the AP 10, 15, 20, 25, …? (a) 130 (b) 125 (c) 135 (d) 140
4. 4.What is the 10th term of the AP 12, 19, 26, 33, …? (a) 75 (b) 63 (c) 82 (d) 70
5. 5.What is the 12th term of the AP 6, 14, 22, 30, …? (a) 102 (b) 94 (c) 96 (d) 88
6. 6.What is the sum of all the whole numbers from 1 to 90? (a) 4005 (b) 8190 (c) 4095 (d) 4050
7. 7.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2278 (c) 4556 (d) 2279
8. 8.What is the sum of all the whole numbers from 1 to 23? (a) 276 (b) 253 (c) 552 (d) 277
9. 9.Which term of the AP 1, 8, 15, 22, … is 267? (a) 41st (b) 39th (c) 40th (d) 38th
10. 10.What is the missing term in the AP 13, 20, ?, 34, 41? (a) 28 (b) 34 (c) 26 (d) 27
11. 11.What is the 14th term of the AP 7, 13, 19, 25, …? (a) 84 (b) 91 (c) 85 (d) 78
12. 12.What is the sum of all the whole numbers from 1 to 93? (a) 4371 (b) 8742 (c) 4372 (d) 4278
13. 13.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1830 (c) 1800 (d) 1770
14. 14.What is the 30th term of the AP 2, 5, 8, 11, …? (a) 90 (b) 92 (c) 89 (d) 87
15. 15.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 441 (c) 462 (d) 231
16. 16.What is the 31st term of the AP 2, 11, 20, 29, …? (a) 270 (b) 279 (c) 272 (d) 281
17. 17.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 120 (c) 225 (d) 240
18. 18.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 1081 (c) 2256 (d) 1128
19. 19.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 7 (b) 5 (c) 8 (d) 6
20. 20.What is the 40th term of the AP 5, 8, 11, 14, …? (a) 122 (b) 120 (c) 125 (d) 117
21. 21.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 132 (d) 66
22. 22.Which term of the AP 9, 11, 13, 15, … is 71? (a) 34th (b) 32nd (c) 33rd (d) 31st
23. 23.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 162 (c) 342 (d) 171
24. 24.What is the 28th term of the AP 2, 7, 12, 17, …? (a) 140 (b) 135 (c) 142 (d) 137
25. 25.What is the 19th term of the AP 12, 20, 28, 36, …? (a) 156 (b) 152 (c) 144 (d) 164
26. 26.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 7140 (c) 3570 (d) 3486
27. 27.What is the sum of all the whole numbers from 1 to 46? (a) 1058 (b) 2162 (c) 1081 (d) 1035
28. 28.What is the 18th term of the AP 9, 14, 19, 24, …? (a) 90 (b) 99 (c) 85 (d) 94
29. 29.What is the 36th term of the AP 1, 9, 17, 25, …? (a) 281 (b) 288 (c) 280 (d) 289
30. 30.What is the 25th term of the AP 7, 12, 17, 22, …? (a) 132 (b) 120 (c) 127 (d) 125
31. 31.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 50 (b) 9 (c) 25 (d) 30
32. 32.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 45 (d) 17
33. 33.Which term of the AP 7, 10, 13, 16, … is 115? (a) 36th (b) 39th (c) 38th (d) 37th
34. 34.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 1560 (c) 780 (d) 781
35. 35.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 150 (b) 27 (c) 90 (d) 75
36. 36.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 288 (b) 576 (c) 46 (d) 312
37. 37.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 650 (c) 49 (d) 325
38. 38.What is the missing term in the AP 16, 20, ?, 28, 32? (a) 28 (b) 23 (c) 25 (d) 24
39. 39.What is the sum of the first 11 terms of the AP 7, 12, 17, …? (a) 357 (b) 352 (c) 704 (d) 57
40. 40.What is the missing term in the AP 2, ?, 16, 23, 30? (a) 9 (b) 16 (c) 8 (d) 10

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