Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 266 · 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 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 81 (d) 90
2. 2.What is the missing term in the AP 16, 23, ?, 37, 44? (a) 31 (b) 37 (c) 30 (d) 29
3. 3.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 14 (b) 100 (c) 50 (d) 55
4. 4.What is the 24th term of the AP 8, 11, 14, 17, …? (a) 69 (b) 80 (c) 77 (d) 72
5. 5.What is the 16th term of the AP 4, 8, 12, 16, …? (a) 60 (b) 65 (c) 64 (d) 68
6. 6.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 65 (b) 120 (c) 22 (d) 60
7. 7.What is the 28th term of the AP 17, 20, 23, 26, …? (a) 84 (b) 81 (c) 101 (d) 98
8. 8.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 112 (b) 63 (c) 56 (d) 14
9. 9.What is the 10th term of the AP 9, 17, 25, 33, …? (a) 72 (b) 81 (c) 89 (d) 80
10. 10.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 78 (c) 92 (d) 91
11. 11.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 22 (b) 18 (c) 19 (d) 17
12. 12.What is the missing term in the AP 18, ?, 30, 36, 42? (a) 30 (b) 23 (c) 24 (d) 25
13. 13.What is the sum of all the whole numbers from 1 to 85? (a) 3570 (b) 3656 (c) 3655 (d) 7310
14. 14.What is the 11th term of the AP 2, 8, 14, 20, …? (a) 62 (b) 60 (c) 66 (d) 68
15. 15.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 105 (c) 121 (d) 120
16. 16.What is the sum of all the whole numbers from 1 to 16? (a) 120 (b) 136 (c) 272 (d) 128
17. 17.What is the 16th term of the AP 6, 12, 18, 24, …? (a) 102 (b) 97 (c) 90 (d) 96
18. 18.Which term of the AP 7, 9, 11, 13, … is 47? (a) 21st (b) 20th (c) 22nd (d) 23rd
19. 19.What is the 28th term of the AP 8, 10, 12, 14, …? (a) 56 (b) 62 (c) 54 (d) 64
20. 20.What is the 14th term of the AP 1, 4, 7, 10, …? (a) 43 (b) 39 (c) 42 (d) 40
21. 21.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 184 (b) 164 (c) 38 (d) 328
22. 22.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 7 (b) 9 (c) 10 (d) 8
23. 23.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 133 (b) 266 (c) 28 (d) 136
24. 24.Which term of the AP 4, 7, 10, 13, … is 73? (a) 24th (b) 25th (c) 26th (d) 23rd
25. 25.Which term of the AP 3, 12, 21, 30, … is 300? (a) 36th (b) 35th (c) 34th (d) 33rd
26. 26.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 78 (c) 72 (d) 156
27. 27.What is the missing term in the AP 15, 20, ?, 30, 35? (a) 24 (b) 26 (c) 25 (d) 30
28. 28.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 90 (b) 23 (c) 156 (d) 78
29. 29.What is the sum of all the whole numbers from 1 to 24? (a) 600 (b) 288 (c) 276 (d) 300
30. 30.What is the 24th term of the AP 4, 7, 10, 13, …? (a) 73 (b) 69 (c) 76 (d) 72
31. 31.Which term of the AP 18, 20, 22, 24, … is 92? (a) 38th (b) 39th (c) 46th (d) 37th
32. 32.What is the 32nd term of the AP 13, 18, 23, 28, …? (a) 168 (b) 160 (c) 173 (d) 155
33. 33.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 325 (c) 351 (d) 702
34. 34.What is the sum of all the whole numbers from 1 to 70? (a) 4970 (b) 2415 (c) 2450 (d) 2485
35. 35.What is the sum of all the whole numbers from 1 to 95? (a) 4465 (b) 4560 (c) 4561 (d) 9120
36. 36.Which term of the AP 15, 18, 21, 24, … is 60? (a) 17th (b) 16th (c) 15th (d) 20th
37. 37.What is the 32nd term of the AP 6, 8, 10, 12, …? (a) 64 (b) 62 (c) 70 (d) 68
38. 38.Which term of the AP 4, 10, 16, 22, … is 184? (a) 31st (b) 33rd (c) 32nd (d) 30th
39. 39.What is the sum of all the whole numbers from 1 to 29? (a) 406 (b) 435 (c) 436 (d) 870
40. 40.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 47 (d) 576

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