Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 894 · 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 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 210 (c) 420 (d) 39
2. 2.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 198 (b) 24 (c) 99 (d) 108
3. 3.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 462 (d) 41
4. 4.What is the 12th term of the AP 4, 9, 14, 19, …? (a) 60 (b) 59 (c) 64 (d) 55
5. 5.What is the 25th term of the AP 1, 7, 13, 19, …? (a) 150 (b) 144 (c) 145 (d) 151
6. 6.What is the 13th term of the AP 19, 21, 23, 25, …? (a) 24 (b) 45 (c) 26 (d) 43
7. 7.What is the 22nd term of the AP 8, 16, 24, 32, …? (a) 184 (b) 176 (c) 168 (d) 177
8. 8.What is the sum of all the whole numbers from 1 to 68? (a) 2312 (b) 2278 (c) 4692 (d) 2346
9. 9.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 1654 (c) 3306 (d) 1653
10. 10.Which term of the AP 10, 18, 26, 34, … is 98? (a) 12th (b) 13th (c) 11th (d) 14th
11. 11.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 66 (b) 13 (c) 63 (d) 126
12. 12.What is the 20th term of the AP 12, 17, 22, 27, …? (a) 112 (b) 100 (c) 95 (d) 107
13. 13.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 46 (b) 260 (c) 235 (d) 470
14. 14.What is the 33rd term of the AP 18, 27, 36, 45, …? (a) 288 (b) 297 (c) 315 (d) 306
15. 15.What is the 34th term of the AP 2, 6, 10, 14, …? (a) 132 (b) 134 (c) 136 (d) 138
16. 16.What is the 19th term of the AP 17, 26, 35, 44, …? (a) 171 (b) 162 (c) 188 (d) 179
17. 17.Which term of the AP 2, 10, 18, 26, … is 226? (a) 28th (b) 31st (c) 30th (d) 29th
18. 18.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 33 (d) 289
19. 19.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 812 (c) 55 (d) 406
20. 20.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 23 (b) 26 (c) 24 (d) 22
21. 21.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 114 (b) 17 (c) 66 (d) 57
22. 22.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
23. 23.What is the 27th term of the AP 9, 16, 23, 30, …? (a) 189 (b) 182 (c) 191 (d) 198
24. 24.What is the 12th term of the AP 18, 26, 34, 42, …? (a) 106 (b) 114 (c) 88 (d) 96
25. 25.What is the sum of all the whole numbers from 1 to 58? (a) 1711 (b) 3422 (c) 1653 (d) 1682
26. 26.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 6 (b) 8 (c) 7 (d) 5
27. 27.Which term of the AP 14, 16, 18, 20, … is 90? (a) 39th (b) 38th (c) 45th (d) 40th
28. 28.What is the 36th term of the AP 1, 4, 7, 10, …? (a) 105 (b) 109 (c) 108 (d) 106
29. 29.What is the 17th term of the AP 18, 21, 24, 27, …? (a) 69 (b) 51 (c) 48 (d) 66
30. 30.What is the 15th term of the AP 4, 7, 10, 13, …? (a) 42 (b) 45 (c) 46 (d) 49
31. 31.What is the 14th term of the AP 5, 14, 23, 32, …? (a) 131 (b) 122 (c) 117 (d) 126
32. 32.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 384 (b) 768 (c) 54 (d) 408
33. 33.What is the 34th term of the AP 2, 9, 16, 23, …? (a) 233 (b) 240 (c) 238 (d) 231
34. 34.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 702 (c) 325 (d) 338
35. 35.What is the 22nd term of the AP 7, 9, 11, 13, …? (a) 49 (b) 42 (c) 51 (d) 44
36. 36.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 7482 (c) 3698 (d) 3741
37. 37.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 2070 (c) 1035 (d) 990
38. 38.What is the missing term in the AP 4, 10, 16, ?, 28? (a) 21 (b) 23 (c) 22 (d) 28
39. 39.What is the missing term in the AP 9, 16, ?, 30, 37? (a) 22 (b) 30 (c) 24 (d) 23
40. 40.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 562 (c) 561 (d) 1122

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