Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 980 · 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 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 676 (c) 51 (d) 351
2. 2.What is the missing term in the AP 11, 15, ?, 23, 27? (a) 18 (b) 20 (c) 23 (d) 19
3. 3.What is the 37th term of the AP 11, 19, 27, 35, …? (a) 299 (b) 307 (c) 296 (d) 288
4. 4.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 2701 (c) 2775 (d) 5550
5. 5.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 784 (d) 55
6. 6.What is the 11th term of the AP 6, 13, 20, 27, …? (a) 83 (b) 70 (c) 76 (d) 77
7. 7.What is the 13th term of the AP 1, 10, 19, 28, …? (a) 109 (b) 118 (c) 108 (d) 117
8. 8.What is the missing term in the AP 11, 14, ?, 20, 23? (a) 16 (b) 18 (c) 17 (d) 20
9. 9.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 4753 (c) 9506 (d) 4754
10. 10.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 105 (d) 196
11. 11.What is the 21st term of the AP 19, 21, 23, 25, …? (a) 40 (b) 59 (c) 42 (d) 61
12. 12.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 529 (c) 45 (d) 276
13. 13.What is the 34th term of the AP 9, 15, 21, 27, …? (a) 213 (b) 198 (c) 204 (d) 207
14. 14.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 3306 (c) 1654 (d) 1596
15. 15.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 51 (b) 243 (c) 486 (d) 270
16. 16.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 325 (c) 351 (d) 702
17. 17.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 20 (b) 18 (c) 19 (d) 26
18. 18.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 43 (b) 196 (c) 350 (d) 175
19. 19.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 870 (d) 841
20. 20.What is the 24th term of the AP 9, 12, 15, 18, …? (a) 78 (b) 69 (c) 81 (d) 72
21. 21.Which term of the AP 3, 12, 21, 30, … is 102? (a) 13th (b) 11th (c) 14th (d) 12th
22. 22.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3321 (c) 3240 (d) 3322
23. 23.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 15 (b) 17 (c) 13 (d) 14
24. 24.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 12 (b) 14 (c) 10 (d) 11
25. 25.What is the 17th term of the AP 17, 19, 21, 23, …? (a) 51 (b) 32 (c) 34 (d) 49
26. 26.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 267 (b) 528 (c) 39 (d) 264
27. 27.What is the 32nd term of the AP 7, 10, 13, 16, …? (a) 93 (b) 100 (c) 103 (d) 96
28. 28.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 109 (b) 16 (c) 216 (d) 108
29. 29.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 289 (d) 33
30. 30.What is the 31st term of the AP 12, 18, 24, 30, …? (a) 198 (b) 192 (c) 180 (d) 186
31. 31.What is the 32nd term of the AP 9, 18, 27, 36, …? (a) 289 (b) 279 (c) 288 (d) 297
32. 32.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 144 (b) 288 (c) 162 (d) 39
33. 33.What is the 34th term of the AP 18, 25, 32, 39, …? (a) 238 (b) 249 (c) 231 (d) 256
34. 34.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 361 (c) 190 (d) 380
35. 35.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 300 (c) 600 (d) 47
36. 36.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 729 (d) 756
37. 37.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 102 (b) 174 (c) 27 (d) 87
38. 38.Which term of the AP 19, 23, 27, 31, … is 151? (a) 33rd (b) 35th (c) 34th (d) 36th
39. 39.What is the 26th term of the AP 20, 25, 30, 35, …? (a) 150 (b) 125 (c) 145 (d) 130
40. 40.What is the 34th term of the AP 8, 17, 26, 35, …? (a) 314 (b) 306 (c) 305 (d) 297

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