Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 74 · 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 34th term of the AP 11, 14, 17, 20, …? (a) 102 (b) 99 (c) 113 (d) 110
2. 2.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 19 (b) 96 (c) 192 (d) 104
3. 3.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 143 (b) 144 (c) 18 (d) 286
4. 4.What is the 18th term of the AP 5, 11, 17, 23, …? (a) 108 (b) 102 (c) 107 (d) 113
5. 5.What is the missing term in the AP 7, 14, 21, ?, 35? (a) 29 (b) 28 (c) 35 (d) 27
6. 6.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 870 (c) 57 (d) 841
7. 7.What is the 35th term of the AP 11, 13, 15, 17, …? (a) 70 (b) 68 (c) 79 (d) 81
8. 8.Which term of the AP 8, 11, 14, 17, … is 104? (a) 32nd (b) 35th (c) 33rd (d) 34th
9. 9.What is the 28th term of the AP 3, 9, 15, 21, …? (a) 165 (b) 162 (c) 171 (d) 168
10. 10.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 480 (b) 31 (c) 240 (d) 252
11. 11.What is the missing term in the AP 20, 22, ?, 26, 28? (a) 24 (b) 23 (c) 25 (d) 26
12. 12.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 1770 (c) 1771 (d) 3540
13. 13.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 29 (b) 114 (c) 99 (d) 198
14. 14.What is the 12th term of the AP 6, 9, 12, 15, …? (a) 39 (b) 36 (c) 33 (d) 42
15. 15.What is the 33rd term of the AP 14, 23, 32, 41, …? (a) 288 (b) 311 (c) 302 (d) 297
16. 16.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3741 (c) 3655 (d) 7482
17. 17.What is the missing term in the AP 13, 22, ?, 40, 49? (a) 30 (b) 40 (c) 31 (d) 32
18. 18.Which term of the AP 1, 10, 19, 28, … is 118? (a) 13th (b) 16th (c) 15th (d) 14th
19. 19.Which term of the AP 11, 15, 19, 23, … is 63? (a) 16th (b) 14th (c) 15th (d) 13th
20. 20.Which term of the AP 3, 6, 9, 12, … is 120? (a) 41st (b) 42nd (c) 39th (d) 40th
21. 21.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 361 (c) 190 (d) 380
22. 22.What is the sum of the first 10 terms of the AP 7, 12, 17, …? (a) 52 (b) 590 (c) 320 (d) 295
23. 23.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 703 (c) 722 (d) 1482
24. 24.Which term of the AP 17, 25, 33, 41, … is 193? (a) 23rd (b) 24th (c) 22nd (d) 25th
25. 25.What is the 34th term of the AP 9, 15, 21, 27, …? (a) 198 (b) 204 (c) 213 (d) 207
26. 26.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 300 (c) 600 (d) 576
27. 27.What is the sum of all the whole numbers from 1 to 88? (a) 3916 (b) 3872 (c) 3828 (d) 7832
28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 56 (c) 28 (d) 13
29. 29.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 625 (c) 49 (d) 325
30. 30.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 11 (b) 13 (c) 12 (d) 10
31. 31.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 390 (b) 420 (c) 780 (d) 60
32. 32.What is the 20th term of the AP 9, 14, 19, 24, …? (a) 100 (b) 104 (c) 109 (d) 95
33. 33.Which term of the AP 7, 9, 11, 13, … is 45? (a) 19th (b) 21st (c) 22nd (d) 20th
34. 34.What is the sum of all the whole numbers from 1 to 67? (a) 4556 (b) 2211 (c) 2279 (d) 2278
35. 35.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 484 (c) 506 (d) 43
36. 36.What is the 31st term of the AP 1, 8, 15, 22, …? (a) 210 (b) 217 (c) 211 (d) 218
37. 37.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 57 (b) 66 (c) 17 (d) 114
38. 38.What is the 27th term of the AP 3, 9, 15, 21, …? (a) 162 (b) 156 (c) 165 (d) 159
39. 39.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 24 (b) 198 (c) 99 (d) 108
40. 40.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 49 (b) 224 (c) 448 (d) 248

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