Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 703 · 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 15, ?, 29, 36, 43? (a) 21 (b) 29 (c) 23 (d) 22
2. 2.What is the 24th term of the AP 9, 16, 23, 30, …? (a) 168 (b) 161 (c) 177 (d) 170
3. 3.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1682 (c) 1711 (d) 1653
4. 4.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 812 (d) 784
5. 5.What is the missing term in the AP 11, 15, 19, ?, 27? (a) 23 (b) 22 (c) 27 (d) 24
6. 6.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 144 (d) 78
7. 7.Which term of the AP 15, 18, 21, 24, … is 132? (a) 39th (b) 44th (c) 40th (d) 41st
8. 8.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
9. 9.Which term of the AP 6, 13, 20, 27, … is 76? (a) 12th (b) 10th (c) 11th (d) 13th
10. 10.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 23 (b) 256 (c) 128 (d) 136
11. 11.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 576 (c) 600 (d) 47
12. 12.Which term of the AP 8, 13, 18, 23, … is 168? (a) 33rd (b) 32nd (c) 34th (d) 35th
13. 13.What is the sum of the first 7 terms of the AP 5, 10, 15, …? (a) 140 (b) 35 (c) 280 (d) 145
14. 14.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 8 (b) 6 (c) 10 (d) 7
15. 15.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 66 (c) 121 (d) 21
16. 16.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 12 (b) 150 (c) 80 (d) 75
17. 17.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 756 (c) 53 (d) 729
18. 18.What is the 21st term of the AP 20, 22, 24, 26, …? (a) 42 (b) 62 (c) 40 (d) 60
19. 19.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 14 (b) 16 (c) 13 (d) 12
20. 20.What is the 33rd term of the AP 1, 5, 9, 13, …? (a) 133 (b) 128 (c) 132 (d) 129
21. 21.Which term of the AP 12, 18, 24, 30, … is 60? (a) 9th (b) 8th (c) 11th (d) 10th
22. 22.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 130 (b) 19 (c) 65 (d) 68
23. 23.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 1378 (c) 2756 (d) 1352
24. 24.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 324 (c) 342 (d) 171
25. 25.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 15 (d) 25
26. 26.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 441 (c) 41 (d) 231
27. 27.What is the 20th term of the AP 16, 19, 22, 25, …? (a) 60 (b) 76 (c) 57 (d) 73
28. 28.Which term of the AP 20, 24, 28, 32, … is 100? (a) 22nd (b) 20th (c) 25th (d) 21st
29. 29.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 210 (d) 105
30. 30.What is the 27th term of the AP 10, 17, 24, 31, …? (a) 189 (b) 192 (c) 199 (d) 182
31. 31.Which term of the AP 2, 8, 14, 20, … is 98? (a) 16th (b) 17th (c) 18th (d) 19th
32. 32.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 5112 (c) 2557 (d) 2485
33. 33.What is the 40th term of the AP 16, 18, 20, 22, …? (a) 94 (b) 78 (c) 80 (d) 96
34. 34.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 14 (b) 60 (c) 61 (d) 120
35. 35.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 435 (c) 57 (d) 870
36. 36.What is the sum of all the whole numbers from 1 to 97? (a) 4753 (b) 4754 (c) 4656 (d) 9506
37. 37.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 231 (c) 242 (d) 253
38. 38.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 506 (c) 43 (d) 253
39. 39.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 756 (c) 351 (d) 378
40. 40.What is the missing term in the AP 9, 18, 27, ?, 45? (a) 35 (b) 45 (c) 37 (d) 36

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