Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 7 · 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 12 terms of the AP 10, 12, 14, …? (a) 252 (b) 264 (c) 32 (d) 504
2. 2.What is the 40th term of the AP 3, 12, 21, 30, …? (a) 354 (b) 351 (c) 363 (d) 360
3. 3.What is the sum of the first 8 terms of the AP 4, 8, 12, …? (a) 32 (b) 288 (c) 160 (d) 144
4. 4.What is the 11th term of the AP 5, 14, 23, 32, …? (a) 95 (b) 90 (c) 99 (d) 104
5. 5.What is the 37th term of the AP 18, 23, 28, 33, …? (a) 203 (b) 185 (c) 198 (d) 180
6. 6.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 324 (d) 35
7. 7.What is the 19th term of the AP 7, 11, 15, 19, …? (a) 76 (b) 72 (c) 79 (d) 83
8. 8.Which term of the AP 12, 17, 22, 27, … is 82? (a) 17th (b) 15th (c) 14th (d) 16th
9. 9.What is the sum of all the whole numbers from 1 to 36? (a) 630 (b) 1332 (c) 666 (d) 648
10. 10.What is the 24th term of the AP 13, 17, 21, 25, …? (a) 105 (b) 92 (c) 109 (d) 96
11. 11.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 4418 (c) 8930 (d) 4371
12. 12.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 17 (b) 66 (c) 57 (d) 114
13. 13.What is the 27th term of the AP 5, 8, 11, 14, …? (a) 78 (b) 81 (c) 83 (d) 86
14. 14.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 4 (b) 7 (c) 3 (d) 5
15. 15.What is the missing term in the AP 15, 23, ?, 39, 47? (a) 39 (b) 32 (c) 30 (d) 31
16. 16.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 144 (b) 132 (c) 27 (d) 264
17. 17.What is the missing term in the AP 19, ?, 23, 25, 27? (a) 22 (b) 20 (c) 21 (d) 23
18. 18.What is the 39th term of the AP 2, 10, 18, 26, …? (a) 314 (b) 304 (c) 306 (d) 312
19. 19.What is the 10th term of the AP 9, 14, 19, 24, …? (a) 54 (b) 45 (c) 59 (d) 50
20. 20.What is the missing term in the AP 5, ?, 23, 32, 41? (a) 14 (b) 15 (c) 13 (d) 23
21. 21.What is the 10th term of the AP 9, 12, 15, 18, …? (a) 30 (b) 27 (c) 36 (d) 39
22. 22.What is the 36th term of the AP 5, 12, 19, 26, …? (a) 245 (b) 250 (c) 257 (d) 252
23. 23.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1432 (c) 1431 (d) 2862
24. 24.What is the 15th term of the AP 15, 19, 23, 27, …? (a) 75 (b) 56 (c) 71 (d) 60
25. 25.What is the 21st term of the AP 9, 18, 27, 36, …? (a) 198 (b) 190 (c) 189 (d) 180
26. 26.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 682 (b) 341 (c) 61 (d) 374
27. 27.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 4851 (c) 9900 (d) 4951
28. 28.What is the 37th term of the AP 13, 15, 17, 19, …? (a) 85 (b) 87 (c) 72 (d) 74
29. 29.What is the 32nd term of the AP 5, 11, 17, 23, …? (a) 197 (b) 186 (c) 191 (d) 192
30. 30.What is the 39th term of the AP 3, 6, 9, 12, …? (a) 118 (b) 117 (c) 120 (d) 114
31. 31.What is the missing term in the AP 14, 22, 30, ?, 46? (a) 46 (b) 39 (c) 38 (d) 37
32. 32.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 186 (b) 93 (c) 102 (d) 23
33. 33.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 276 (c) 253 (d) 277
34. 34.What is the 19th term of the AP 20, 23, 26, 29, …? (a) 77 (b) 54 (c) 74 (d) 57
35. 35.What is the 31st term of the AP 1, 9, 17, 25, …? (a) 249 (b) 248 (c) 240 (d) 241
36. 36.What is the missing term in the AP 5, 11, 17, ?, 29? (a) 23 (b) 22 (c) 24 (d) 29
37. 37.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 68 (b) 456 (c) 840 (d) 420
38. 38.Which term of the AP 3, 10, 17, 24, … is 192? (a) 29th (b) 28th (c) 30th (d) 27th
39. 39.What is the 23rd term of the AP 12, 21, 30, 39, …? (a) 207 (b) 198 (c) 219 (d) 210
40. 40.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 361 (d) 380

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