Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 83 · 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 15th term of the AP 10, 14, 18, 22, …? (a) 56 (b) 66 (c) 60 (d) 70
2. 2.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 66 (c) 67 (d) 55
3. 3.Which term of the AP 17, 22, 27, 32, … is 167? (a) 33rd (b) 31st (c) 30th (d) 32nd
4. 4.What is the 25th term of the AP 19, 23, 27, 31, …? (a) 115 (b) 100 (c) 96 (d) 119
5. 5.What is the missing term in the AP 16, ?, 20, 22, 24? (a) 19 (b) 20 (c) 17 (d) 18
6. 6.What is the 34th term of the AP 14, 18, 22, 26, …? (a) 136 (b) 146 (c) 132 (d) 150
7. 7.What is the 19th term of the AP 15, 19, 23, 27, …? (a) 76 (b) 91 (c) 72 (d) 87
8. 8.What is the 40th term of the AP 1, 9, 17, 25, …? (a) 321 (b) 320 (c) 313 (d) 312
9. 9.What is the missing term in the AP 20, 22, 24, ?, 28? (a) 28 (b) 26 (c) 25 (d) 27
10. 10.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 841 (d) 870
11. 11.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 9 (b) 10 (c) 15 (d) 8
12. 12.What is the 34th term of the AP 6, 15, 24, 33, …? (a) 303 (b) 297 (c) 312 (d) 306
13. 13.What is the 31st term of the AP 5, 12, 19, 26, …? (a) 222 (b) 210 (c) 217 (d) 215
14. 14.What is the 40th term of the AP 20, 27, 34, 41, …? (a) 293 (b) 273 (c) 300 (d) 280
15. 15.What is the 11th term of the AP 13, 16, 19, 22, …? (a) 46 (b) 43 (c) 33 (d) 30
16. 16.What is the 39th term of the AP 6, 14, 22, 30, …? (a) 304 (b) 312 (c) 310 (d) 318
17. 17.Which term of the AP 2, 5, 8, 11, … is 104? (a) 35th (b) 37th (c) 36th (d) 34th
18. 18.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 676 (d) 702
19. 19.What is the sum of the first 11 terms of the AP 10, 16, 22, …? (a) 880 (b) 70 (c) 440 (d) 473
20. 20.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 35 (b) 270 (c) 135 (d) 150
21. 21.What is the missing term in the AP 5, 9, ?, 17, 21? (a) 17 (b) 14 (c) 13 (d) 12
22. 22.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 73 (b) 140 (c) 20 (d) 70
23. 23.Which term of the AP 12, 19, 26, 33, … is 187? (a) 25th (b) 28th (c) 27th (d) 26th
24. 24.What is the 22nd term of the AP 1, 6, 11, 16, …? (a) 110 (b) 105 (c) 111 (d) 106
25. 25.Which term of the AP 4, 10, 16, 22, … is 46? (a) 7th (b) 10th (c) 8th (d) 9th
26. 26.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 12 (b) 136 (c) 72 (d) 68
27. 27.What is the 10th term of the AP 7, 10, 13, 16, …? (a) 37 (b) 30 (c) 27 (d) 34
28. 28.What is the 31st term of the AP 8, 14, 20, 26, …? (a) 194 (b) 180 (c) 188 (d) 186
29. 29.What is the missing term in the AP 3, 5, ?, 9, 11? (a) 8 (b) 6 (c) 9 (d) 7
30. 30.Which term of the AP 5, 12, 19, 26, … is 145? (a) 22nd (b) 20th (c) 21st (d) 23rd
31. 31.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 132 (c) 21 (d) 66
32. 32.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 3906 (c) 1953 (d) 1891
33. 33.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 9900 (c) 4950 (d) 4851
34. 34.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1327 (c) 1275 (d) 1326
35. 35.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 45 (b) 46 (c) 90 (d) 11
36. 36.What is the missing term in the AP 11, 15, 19, ?, 27? (a) 27 (b) 22 (c) 23 (d) 24
37. 37.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 30 (b) 25 (c) 50 (d) 9
38. 38.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 136 (c) 153 (d) 154
39. 39.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 5 (b) 4 (c) 7 (d) 6
40. 40.What is the 19th term of the AP 13, 16, 19, 22, …? (a) 54 (b) 57 (c) 67 (d) 70

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