Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 564 · 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 28th term of the AP 3, 7, 11, 15, …? (a) 108 (b) 112 (c) 111 (d) 115
2. 2.What is the 12th term of the AP 5, 11, 17, 23, …? (a) 77 (b) 72 (c) 71 (d) 66
3. 3.What is the missing term in the AP 15, 19, 23, ?, 31? (a) 27 (b) 31 (c) 26 (d) 28
4. 4.What is the 30th term of the AP 4, 6, 8, 10, …? (a) 58 (b) 60 (c) 62 (d) 64
5. 5.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 990 (c) 1035 (d) 2070
6. 6.What is the 31st term of the AP 1, 7, 13, 19, …? (a) 180 (b) 187 (c) 181 (d) 186
7. 7.What is the sum of all the whole numbers from 1 to 92? (a) 4186 (b) 4232 (c) 8556 (d) 4278
8. 8.What is the 30th term of the AP 7, 9, 11, 13, …? (a) 58 (b) 60 (c) 65 (d) 67
9. 9.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 112 (b) 31 (c) 224 (d) 117
10. 10.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 650 (c) 325 (d) 49
11. 11.What is the 19th term of the AP 1, 8, 15, 22, …? (a) 133 (b) 127 (c) 126 (d) 134
12. 12.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 59 (c) 465 (d) 900
13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 841 (d) 870
14. 14.Which term of the AP 4, 11, 18, 25, … is 228? (a) 35th (b) 33rd (c) 34th (d) 32nd
15. 15.What is the 15th term of the AP 12, 17, 22, 27, …? (a) 82 (b) 75 (c) 87 (d) 70
16. 16.What is the 13th term of the AP 13, 16, 19, 22, …? (a) 39 (b) 49 (c) 52 (d) 36
17. 17.Which term of the AP 18, 21, 24, 27, … is 132? (a) 38th (b) 40th (c) 39th (d) 44th
18. 18.What is the missing term in the AP 1, 4, ?, 10, 13? (a) 8 (b) 7 (c) 10 (d) 6
19. 19.What is the 31st term of the AP 15, 17, 19, 21, …? (a) 60 (b) 75 (c) 77 (d) 62
20. 20.What is the 21st term of the AP 8, 12, 16, 20, …? (a) 88 (b) 84 (c) 92 (d) 80
21. 21.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 612 (b) 42 (c) 324 (d) 306
22. 22.What is the 31st term of the AP 3, 6, 9, 12, …? (a) 96 (b) 90 (c) 94 (d) 93
23. 23.What is the missing term in the AP 6, 14, 22, ?, 38? (a) 31 (b) 30 (c) 38 (d) 29
24. 24.What is the missing term in the AP 11, 13, 15, ?, 19? (a) 16 (b) 18 (c) 17 (d) 19
25. 25.Which term of the AP 20, 26, 32, 38, … is 62? (a) 8th (b) 7th (c) 10th (d) 9th
26. 26.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 160 (b) 80 (c) 88 (d) 17
27. 27.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 30 (b) 16 (c) 5 (d) 15
28. 28.What is the 14th term of the AP 8, 17, 26, 35, …? (a) 126 (b) 117 (c) 134 (d) 125
29. 29.What is the 11th term of the AP 19, 27, 35, 43, …? (a) 107 (b) 88 (c) 99 (d) 80
30. 30.What is the 17th term of the AP 16, 21, 26, 31, …? (a) 85 (b) 101 (c) 80 (d) 96
31. 31.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 66 (c) 21 (d) 132
32. 32.What is the 27th term of the AP 12, 17, 22, 27, …? (a) 142 (b) 147 (c) 135 (d) 130
33. 33.What is the 37th term of the AP 2, 4, 6, 8, …? (a) 74 (b) 76 (c) 75 (d) 72
34. 34.What is the 21st term of the AP 14, 20, 26, 32, …? (a) 140 (b) 134 (c) 120 (d) 126
35. 35.What is the 30th term of the AP 5, 7, 9, 11, …? (a) 60 (b) 65 (c) 63 (d) 58
36. 36.What is the sum of the first 8 terms of the AP 4, 7, 10, …? (a) 116 (b) 25 (c) 232 (d) 128
37. 37.What is the missing term in the AP 9, ?, 19, 24, 29? (a) 19 (b) 13 (c) 15 (d) 14
38. 38.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 120 (b) 16 (c) 65 (d) 60
39. 39.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 19 (b) 14 (c) 15 (d) 16
40. 40.What is the 20th term of the AP 15, 18, 21, 24, …? (a) 60 (b) 75 (c) 57 (d) 72

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