Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 665 · 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 all the whole numbers from 1 to 83? (a) 3403 (b) 3486 (c) 3487 (d) 6972
2. 2.What is the 35th term of the AP 17, 25, 33, 41, …? (a) 272 (b) 280 (c) 289 (d) 297
3. 3.What is the 38th term of the AP 9, 11, 13, 15, …? (a) 74 (b) 76 (c) 83 (d) 85
4. 4.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 17 (b) 19 (c) 26 (d) 18
5. 5.What is the 13th term of the AP 9, 12, 15, 18, …? (a) 45 (b) 36 (c) 48 (d) 39
6. 6.What is the 34th term of the AP 6, 13, 20, 27, …? (a) 244 (b) 237 (c) 231 (d) 238
7. 7.What is the missing term in the AP 18, ?, 24, 27, 30? (a) 21 (b) 22 (c) 20 (d) 24
8. 8.What is the 34th term of the AP 10, 16, 22, 28, …? (a) 204 (b) 214 (c) 208 (d) 198
9. 9.What is the missing term in the AP 19, 24, ?, 34, 39? (a) 28 (b) 29 (c) 34 (d) 30
10. 10.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 231 (c) 462 (d) 41
11. 11.What is the 40th term of the AP 5, 8, 11, 14, …? (a) 125 (b) 122 (c) 117 (d) 120
12. 12.What is the missing term in the AP 4, 8, 12, ?, 20? (a) 17 (b) 15 (c) 20 (d) 16
13. 13.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 148 (b) 168 (c) 36 (d) 296
14. 14.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 51 (b) 100 (c) 12 (d) 50
15. 15.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 192 (b) 33 (c) 189 (d) 378
16. 16.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 4754 (c) 9506 (d) 4753
17. 17.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 198 (b) 99 (c) 24 (d) 108
18. 18.What is the 27th term of the AP 10, 19, 28, 37, …? (a) 234 (b) 243 (c) 244 (d) 253
19. 19.What is the missing term in the AP 6, ?, 20, 27, 34? (a) 12 (b) 14 (c) 13 (d) 20
20. 20.Which term of the AP 18, 22, 26, 30, … is 158? (a) 35th (b) 37th (c) 38th (d) 36th
21. 21.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 576 (c) 47 (d) 300
22. 22.What is the sum of all the whole numbers from 1 to 37? (a) 1406 (b) 703 (c) 704 (d) 666
23. 23.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 28 (c) 13 (d) 56
24. 24.What is the missing term in the AP 5, 9, 13, ?, 21? (a) 18 (b) 17 (c) 21 (d) 16
25. 25.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 5 (b) 4 (c) 7 (d) 6
26. 26.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 756 (d) 53
27. 27.What is the sum of all the whole numbers from 1 to 90? (a) 8190 (b) 4050 (c) 4095 (d) 4005
28. 28.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 140 (b) 24 (c) 75 (d) 70
29. 29.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3916 (c) 3828 (d) 7832
30. 30.Which term of the AP 12, 20, 28, 36, … is 100? (a) 12th (b) 13th (c) 11th (d) 14th
31. 31.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 23 (b) 154 (c) 286 (d) 143
32. 32.What is the sum of the first 11 terms of the AP 6, 9, 12, …? (a) 36 (b) 462 (c) 234 (d) 231
33. 33.What is the 12th term of the AP 20, 28, 36, 44, …? (a) 96 (b) 88 (c) 116 (d) 108
34. 34.Which term of the AP 11, 19, 27, 35, … is 323? (a) 42nd (b) 41st (c) 40th (d) 39th
35. 35.What is the 21st term of the AP 8, 12, 16, 20, …? (a) 80 (b) 88 (c) 84 (d) 92
36. 36.Which term of the AP 10, 16, 22, 28, … is 52? (a) 7th (b) 10th (c) 9th (d) 8th
37. 37.Which term of the AP 18, 27, 36, 45, … is 99? (a) 10th (b) 9th (c) 11th (d) 12th
38. 38.What is the 40th term of the AP 10, 15, 20, 25, …? (a) 195 (b) 205 (c) 200 (d) 210
39. 39.What is the 39th term of the AP 18, 23, 28, 33, …? (a) 190 (b) 208 (c) 213 (d) 195
40. 40.What is the 38th term of the AP 18, 23, 28, 33, …? (a) 203 (b) 185 (c) 190 (d) 208

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad