Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 561 · 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 13th term of the AP 12, 21, 30, 39, …? (a) 129 (b) 117 (c) 108 (d) 120
2. 2.What is the 27th term of the AP 7, 10, 13, 16, …? (a) 88 (b) 78 (c) 81 (d) 85
3. 3.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 91 (c) 169 (d) 182
4. 4.What is the 37th term of the AP 3, 5, 7, 9, …? (a) 72 (b) 77 (c) 75 (d) 74
5. 5.What is the 23rd term of the AP 13, 21, 29, 37, …? (a) 176 (b) 189 (c) 197 (d) 184
6. 6.What is the missing term in the AP 11, 20, 29, ?, 47? (a) 47 (b) 38 (c) 39 (d) 37
7. 7.What is the 21st term of the AP 1, 4, 7, 10, …? (a) 64 (b) 61 (c) 60 (d) 63
8. 8.What is the 21st term of the AP 16, 20, 24, 28, …? (a) 84 (b) 100 (c) 80 (d) 96
9. 9.What is the 15th term of the AP 11, 14, 17, 20, …? (a) 56 (b) 42 (c) 53 (d) 45
10. 10.What is the 14th term of the AP 9, 15, 21, 27, …? (a) 78 (b) 93 (c) 84 (d) 87
11. 11.What is the missing term in the AP 20, 26, ?, 38, 44? (a) 31 (b) 32 (c) 33 (d) 38
12. 12.Which term of the AP 17, 21, 25, 29, … is 53? (a) 11th (b) 12th (c) 10th (d) 9th
13. 13.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 484 (d) 253
14. 14.Which term of the AP 7, 14, 21, 28, … is 98? (a) 14th (b) 13th (c) 15th (d) 16th
15. 15.What is the missing term in the AP 4, ?, 14, 19, 24? (a) 10 (b) 14 (c) 8 (d) 9
16. 16.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 55 (c) 67 (d) 132
17. 17.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 130 (b) 75 (c) 65 (d) 21
18. 18.Which term of the AP 20, 29, 38, 47, … is 281? (a) 30th (b) 31st (c) 32nd (d) 29th
19. 19.What is the missing term in the AP 12, 17, 22, ?, 32? (a) 32 (b) 26 (c) 28 (d) 27
20. 20.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 110 (b) 19 (c) 200 (d) 100
21. 21.Which term of the AP 11, 14, 17, 20, … is 47? (a) 12th (b) 14th (c) 15th (d) 13th
22. 22.What is the missing term in the AP 5, ?, 21, 29, 37? (a) 12 (b) 14 (c) 13 (d) 21
23. 23.Which term of the AP 19, 27, 35, 43, … is 259? (a) 33rd (b) 31st (c) 32nd (d) 30th
24. 24.What is the 39th term of the AP 20, 27, 34, 41, …? (a) 286 (b) 266 (c) 273 (d) 293
25. 25.What is the 38th term of the AP 2, 9, 16, 23, …? (a) 259 (b) 261 (c) 266 (d) 268
26. 26.What is the 30th term of the AP 5, 7, 9, 11, …? (a) 60 (b) 63 (c) 65 (d) 58
27. 27.What is the 12th term of the AP 2, 8, 14, 20, …? (a) 66 (b) 72 (c) 68 (d) 74
28. 28.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 561 (c) 1190 (d) 578
29. 29.What is the 23rd term of the AP 3, 6, 9, 12, …? (a) 66 (b) 72 (c) 70 (d) 69
30. 30.What is the sum of all the whole numbers from 1 to 32? (a) 496 (b) 1056 (c) 528 (d) 512
31. 31.Which term of the AP 7, 9, 11, 13, … is 73? (a) 36th (b) 34th (c) 33rd (d) 35th
32. 32.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 160 (b) 145 (c) 28 (d) 290
33. 33.Which term of the AP 18, 22, 26, 30, … is 54? (a) 12th (b) 11th (c) 10th (d) 9th
34. 34.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 49 (c) 325 (d) 625
35. 35.What is the 38th term of the AP 2, 6, 10, 14, …? (a) 150 (b) 148 (c) 152 (d) 154
36. 36.What is the missing term in the AP 9, 11, 13, ?, 17? (a) 14 (b) 15 (c) 17 (d) 16
37. 37.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 37 (d) 190
38. 38.What is the 34th term of the AP 4, 10, 16, 22, …? (a) 198 (b) 208 (c) 204 (d) 202
39. 39.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 336 (b) 168 (c) 184 (d) 35
40. 40.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 564 (b) 300 (c) 282 (d) 40

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