Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 872 · 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 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 784 (d) 812
2. 2.What is the 11th term of the AP 15, 21, 27, 33, …? (a) 66 (b) 60 (c) 81 (d) 75
3. 3.Which term of the AP 5, 10, 15, 20, … is 70? (a) 13th (b) 14th (c) 16th (d) 15th
4. 4.Which term of the AP 16, 23, 30, 37, … is 163? (a) 23rd (b) 24th (c) 21st (d) 22nd
5. 5.What is the 19th term of the AP 13, 16, 19, 22, …? (a) 70 (b) 67 (c) 54 (d) 57
6. 6.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 19 (b) 17 (c) 22 (d) 18
7. 7.Which term of the AP 11, 14, 17, 20, … is 98? (a) 31st (b) 29th (c) 32nd (d) 30th
8. 8.What is the 19th term of the AP 6, 15, 24, 33, …? (a) 168 (b) 162 (c) 171 (d) 177
9. 9.What is the 15th term of the AP 13, 21, 29, 37, …? (a) 133 (b) 120 (c) 125 (d) 112
10. 10.What is the 33rd term of the AP 3, 11, 19, 27, …? (a) 264 (b) 256 (c) 259 (d) 267
11. 11.Which term of the AP 16, 23, 30, 37, … is 289? (a) 42nd (b) 40th (c) 41st (d) 39th
12. 12.What is the 12th term of the AP 11, 15, 19, 23, …? (a) 59 (b) 44 (c) 48 (d) 55
13. 13.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 15 (b) 228 (c) 120 (d) 114
14. 14.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 15 (d) 36
15. 15.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 55 (c) 50 (d) 45
16. 16.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 11 (b) 64 (c) 63 (d) 126
17. 17.What is the 40th term of the AP 18, 20, 22, 24, …? (a) 78 (b) 98 (c) 80 (d) 96
18. 18.Which term of the AP 14, 18, 22, 26, … is 126? (a) 31st (b) 28th (c) 29th (d) 30th
19. 19.What is the 35th term of the AP 8, 14, 20, 26, …? (a) 210 (b) 204 (c) 218 (d) 212
20. 20.Which term of the AP 14, 17, 20, 23, … is 128? (a) 41st (b) 38th (c) 39th (d) 40th
21. 21.What is the missing term in the AP 7, 12, ?, 22, 27? (a) 18 (b) 16 (c) 22 (d) 17
22. 22.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 456 (b) 228 (c) 30 (d) 240
23. 23.What is the 17th term of the AP 14, 20, 26, 32, …? (a) 102 (b) 110 (c) 96 (d) 116
24. 24.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 170 (b) 160 (c) 25 (d) 320
25. 25.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 176 (b) 160 (c) 320 (d) 34
26. 26.What is the missing term in the AP 8, 10, ?, 14, 16? (a) 12 (b) 14 (c) 11 (d) 13
27. 27.What is the 10th term of the AP 6, 12, 18, 24, …? (a) 66 (b) 54 (c) 60 (d) 61
28. 28.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 7832 (c) 3916 (d) 3828
29. 29.What is the 21st term of the AP 10, 15, 20, 25, …? (a) 110 (b) 115 (c) 105 (d) 100
30. 30.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 210 (d) 196
31. 31.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 306 (c) 153 (d) 154
32. 32.What is the missing term in the AP 13, 17, ?, 25, 29? (a) 20 (b) 25 (c) 21 (d) 22
33. 33.What is the 18th term of the AP 17, 24, 31, 38, …? (a) 136 (b) 126 (c) 119 (d) 143
34. 34.What is the missing term in the AP 13, 18, 23, ?, 33? (a) 28 (b) 33 (c) 27 (d) 29
35. 35.Which term of the AP 2, 5, 8, 11, … is 38? (a) 15th (b) 12th (c) 14th (d) 13th
36. 36.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 352 (b) 385 (c) 62 (d) 704
37. 37.What is the missing term in the AP 8, ?, 18, 23, 28? (a) 12 (b) 13 (c) 14 (d) 18
38. 38.What is the 18th term of the AP 2, 5, 8, 11, …? (a) 53 (b) 56 (c) 51 (d) 54
39. 39.What is the 21st term of the AP 6, 15, 24, 33, …? (a) 186 (b) 189 (c) 180 (d) 195
40. 40.What is the 24th term of the AP 7, 14, 21, 28, …? (a) 175 (b) 168 (c) 169 (d) 161

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