Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 104 · 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 missing term in the AP 11, 15, 19, ?, 27? (a) 24 (b) 27 (c) 23 (d) 22
2. 2.What is the missing term in the AP 2, 11, 20, ?, 38? (a) 28 (b) 29 (c) 38 (d) 30
3. 3.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 870 (d) 841
4. 4.What is the 28th term of the AP 13, 20, 27, 34, …? (a) 209 (b) 202 (c) 189 (d) 196
5. 5.What is the 16th term of the AP 3, 11, 19, 27, …? (a) 131 (b) 120 (c) 128 (d) 123
6. 6.What is the 23rd term of the AP 20, 29, 38, 47, …? (a) 227 (b) 198 (c) 207 (d) 218
7. 7.What is the 28th term of the AP 20, 24, 28, 32, …? (a) 108 (b) 112 (c) 132 (d) 128
8. 8.What is the missing term in the AP 17, 23, 29, ?, 41? (a) 41 (b) 34 (c) 36 (d) 35
9. 9.What is the 13th term of the AP 5, 10, 15, 20, …? (a) 60 (b) 66 (c) 70 (d) 65
10. 10.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
11. 11.What is the 18th term of the AP 18, 27, 36, 45, …? (a) 180 (b) 171 (c) 162 (d) 153
12. 12.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 190 (c) 380 (d) 191
13. 13.What is the 25th term of the AP 8, 14, 20, 26, …? (a) 150 (b) 144 (c) 158 (d) 152
14. 14.What is the sum of all the whole numbers from 1 to 90? (a) 4005 (b) 4095 (c) 8190 (d) 4050
15. 15.What is the sum of all the whole numbers from 1 to 20? (a) 420 (b) 200 (c) 210 (d) 190
16. 16.What is the 25th term of the AP 2, 4, 6, 8, …? (a) 48 (b) 50 (c) 52 (d) 51
17. 17.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 324 (c) 171 (d) 35
18. 18.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 190 (d) 380
19. 19.What is the 11th term of the AP 15, 20, 25, 30, …? (a) 65 (b) 55 (c) 50 (d) 70
20. 20.Which term of the AP 4, 12, 20, 28, … is 100? (a) 14th (b) 13th (c) 15th (d) 12th
21. 21.What is the missing term in the AP 17, ?, 23, 26, 29? (a) 23 (b) 20 (c) 19 (d) 21
22. 22.Which term of the AP 15, 18, 21, 24, … is 93? (a) 27th (b) 26th (c) 28th (d) 31st
23. 23.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 15 (b) 100 (c) 198 (d) 99
24. 24.What is the 10th term of the AP 8, 11, 14, 17, …? (a) 38 (b) 27 (c) 30 (d) 35
25. 25.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 741 (c) 722 (d) 1482
26. 26.Which term of the AP 11, 14, 17, 20, … is 98? (a) 31st (b) 29th (c) 30th (d) 32nd
27. 27.What is the 39th term of the AP 14, 17, 20, 23, …? (a) 131 (b) 114 (c) 117 (d) 128
28. 28.What is the 29th term of the AP 11, 14, 17, 20, …? (a) 84 (b) 95 (c) 98 (d) 87
29. 29.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 110 (b) 65 (c) 19 (d) 55
30. 30.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 289 (d) 306
31. 31.What is the 29th term of the AP 18, 23, 28, 33, …? (a) 158 (b) 140 (c) 145 (d) 163
32. 32.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3656 (c) 3570 (d) 3655
33. 33.What is the 34th term of the AP 2, 9, 16, 23, …? (a) 240 (b) 233 (c) 231 (d) 238
34. 34.What is the 34th term of the AP 4, 10, 16, 22, …? (a) 198 (b) 204 (c) 208 (d) 202
35. 35.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4561 (c) 4560 (d) 4465
36. 36.What is the 13th term of the AP 3, 5, 7, 9, …? (a) 29 (b) 26 (c) 27 (d) 24
37. 37.Which term of the AP 12, 20, 28, 36, … is 116? (a) 15th (b) 14th (c) 16th (d) 13th
38. 38.What is the 18th term of the AP 2, 9, 16, 23, …? (a) 121 (b) 128 (c) 126 (d) 119
39. 39.What is the missing term in the AP 3, ?, 9, 12, 15? (a) 5 (b) 9 (c) 7 (d) 6
40. 40.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 14 (b) 11 (c) 9 (d) 10

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