Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 490 · 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 18, 24, 30, 36, … is 162? (a) 24th (b) 27th (c) 26th (d) 25th
2. 2.What is the missing term in the AP 8, ?, 18, 23, 28? (a) 12 (b) 13 (c) 18 (d) 14
3. 3.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 17 (b) 81 (c) 90 (d) 162
4. 4.What is the 40th term of the AP 8, 16, 24, 32, …? (a) 328 (b) 312 (c) 320 (d) 321
5. 5.What is the missing term in the AP 15, 20, 25, ?, 35? (a) 30 (b) 31 (c) 29 (d) 35
6. 6.Which term of the AP 15, 19, 23, 27, … is 131? (a) 30th (b) 31st (c) 29th (d) 32nd
7. 7.What is the 12th term of the AP 4, 12, 20, 28, …? (a) 96 (b) 100 (c) 88 (d) 92
8. 8.What is the 22nd term of the AP 14, 18, 22, 26, …? (a) 88 (b) 102 (c) 84 (d) 98
9. 9.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 169 (d) 25
10. 10.What is the 24th term of the AP 10, 17, 24, 31, …? (a) 161 (b) 178 (c) 171 (d) 168
11. 11.What is the sum of the first 12 terms of the AP 10, 15, 20, …? (a) 65 (b) 900 (c) 480 (d) 450
12. 12.What is the 32nd term of the AP 12, 14, 16, 18, …? (a) 64 (b) 76 (c) 74 (d) 62
13. 13.What is the sum of all the whole numbers from 1 to 92? (a) 4186 (b) 4232 (c) 4278 (d) 8556
14. 14.What is the missing term in the AP 9, ?, 23, 30, 37? (a) 16 (b) 17 (c) 15 (d) 23
15. 15.Which term of the AP 11, 14, 17, 20, … is 125? (a) 38th (b) 41st (c) 39th (d) 40th
16. 16.What is the 13th term of the AP 7, 9, 11, 13, …? (a) 33 (b) 24 (c) 26 (d) 31
17. 17.What is the missing term in the AP 17, 19, 21, ?, 25? (a) 24 (b) 22 (c) 23 (d) 25
18. 18.What is the missing term in the AP 11, 17, 23, ?, 35? (a) 30 (b) 29 (c) 35 (d) 28
19. 19.What is the sum of all the whole numbers from 1 to 21? (a) 231 (b) 232 (c) 210 (d) 462
20. 20.What is the 23rd term of the AP 13, 15, 17, 19, …? (a) 59 (b) 46 (c) 57 (d) 44
21. 21.What is the 14th term of the AP 20, 27, 34, 41, …? (a) 111 (b) 98 (c) 118 (d) 91
22. 22.What is the missing term in the AP 5, ?, 13, 17, 21? (a) 13 (b) 8 (c) 10 (d) 9
23. 23.What is the missing term in the AP 9, 17, ?, 33, 41? (a) 26 (b) 24 (c) 25 (d) 33
24. 24.Which term of the AP 16, 21, 26, 31, … is 56? (a) 11th (b) 8th (c) 9th (d) 10th
25. 25.What is the 14th term of the AP 12, 15, 18, 21, …? (a) 51 (b) 54 (c) 42 (d) 39
26. 26.Which term of the AP 5, 9, 13, 17, … is 61? (a) 16th (b) 14th (c) 17th (d) 15th
27. 27.What is the 15th term of the AP 9, 12, 15, 18, …? (a) 42 (b) 51 (c) 54 (d) 45
28. 28.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 378 (c) 406 (d) 392
29. 29.What is the 17th term of the AP 20, 23, 26, 29, …? (a) 51 (b) 48 (c) 68 (d) 71
30. 30.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 266 (b) 133 (c) 154 (d) 37
31. 31.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 35 (d) 342
32. 32.What is the missing term in the AP 10, 12, ?, 16, 18? (a) 16 (b) 15 (c) 13 (d) 14
33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 121 (d) 132
34. 34.What is the 36th term of the AP 12, 15, 18, 21, …? (a) 120 (b) 105 (c) 117 (d) 108
35. 35.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 36 (b) 35 (c) 70 (d) 8
36. 36.What is the 15th term of the AP 13, 17, 21, 25, …? (a) 60 (b) 69 (c) 56 (d) 73
37. 37.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 36 (b) 66 (c) 8 (d) 33
38. 38.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 528 (c) 562 (d) 1122
39. 39.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 350 (b) 180 (c) 40 (d) 175
40. 40.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 784 (d) 406

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