Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 302 · 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 8 terms of the AP 1, 7, 13, …? (a) 352 (b) 43 (c) 176 (d) 200
2. 2.What is the missing term in the AP 16, ?, 32, 40, 48? (a) 24 (b) 25 (c) 23 (d) 32
3. 3.What is the missing term in the AP 9, 11, 13, ?, 17? (a) 16 (b) 17 (c) 15 (d) 14
4. 4.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 84 (b) 75 (c) 20 (d) 150
5. 5.What is the 30th term of the AP 12, 15, 18, 21, …? (a) 102 (b) 90 (c) 87 (d) 99
6. 6.Which term of the AP 9, 11, 13, 15, … is 87? (a) 39th (b) 41st (c) 40th (d) 42nd
7. 7.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 17 (b) 16 (c) 18 (d) 19
8. 8.What is the missing term in the AP 2, ?, 16, 23, 30? (a) 16 (b) 9 (c) 8 (d) 10
9. 9.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 104 (b) 184 (c) 92 (d) 22
10. 10.Which term of the AP 7, 9, 11, 13, … is 65? (a) 30th (b) 32nd (c) 29th (d) 31st
11. 11.Which term of the AP 16, 25, 34, 43, … is 349? (a) 40th (b) 39th (c) 38th (d) 37th
12. 12.What is the 23rd term of the AP 10, 17, 24, 31, …? (a) 164 (b) 154 (c) 161 (d) 171
13. 13.What is the missing term in the AP 2, 7, 12, ?, 22? (a) 16 (b) 22 (c) 18 (d) 17
14. 14.Which term of the AP 11, 17, 23, 29, … is 137? (a) 21st (b) 24th (c) 22nd (d) 23rd
15. 15.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 45 (d) 90
16. 16.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 729 (c) 378 (d) 756
17. 17.What is the 19th term of the AP 2, 5, 8, 11, …? (a) 56 (b) 54 (c) 57 (d) 59
18. 18.What is the 11th term of the AP 17, 19, 21, 23, …? (a) 39 (b) 37 (c) 20 (d) 22
19. 19.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 58 (b) 732 (c) 396 (d) 366
20. 20.What is the 10th term of the AP 8, 14, 20, 26, …? (a) 68 (b) 62 (c) 54 (d) 60
21. 21.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 3403 (c) 6972 (d) 3486
22. 22.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 102 (b) 32 (c) 204 (d) 120
23. 23.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 5 (b) 4 (c) 7 (d) 3
24. 24.What is the 39th term of the AP 11, 17, 23, 29, …? (a) 228 (b) 234 (c) 245 (d) 239
25. 25.Which term of the AP 7, 15, 23, 31, … is 143? (a) 17th (b) 18th (c) 20th (d) 19th
26. 26.What is the 18th term of the AP 1, 3, 5, 7, …? (a) 35 (b) 34 (c) 36 (d) 37
27. 27.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 612 (b) 333 (c) 306 (d) 58
28. 28.What is the 17th term of the AP 9, 17, 25, 33, …? (a) 145 (b) 137 (c) 136 (d) 128
29. 29.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 90 (b) 13 (c) 45 (d) 50
30. 30.What is the missing term in the AP 18, 26, ?, 42, 50? (a) 33 (b) 42 (c) 34 (d) 35
31. 31.What is the missing term in the AP 8, 15, ?, 29, 36? (a) 22 (b) 23 (c) 29 (d) 21
32. 32.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 165 (b) 330 (c) 25 (d) 176
33. 33.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 631 (c) 595 (d) 1260
34. 34.What is the 25th term of the AP 18, 23, 28, 33, …? (a) 138 (b) 143 (c) 125 (d) 120
35. 35.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 9 (b) 12 (c) 8 (d) 10
36. 36.Which term of the AP 20, 26, 32, 38, … is 188? (a) 28th (b) 31st (c) 30th (d) 29th
37. 37.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 99 (b) 24 (c) 108 (d) 198
38. 38.Which term of the AP 8, 12, 16, 20, … is 76? (a) 17th (b) 19th (c) 18th (d) 20th
39. 39.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 110 (c) 50 (d) 55
40. 40.What is the 29th term of the AP 11, 14, 17, 20, …? (a) 87 (b) 95 (c) 84 (d) 98

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