Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 49 · 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.Which term of the AP 3, 9, 15, 21, … is 207? (a) 37th (b) 34th (c) 35th (d) 36th
2. 2.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 100 (b) 105 (c) 30 (d) 200
3. 3.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 231 (b) 30 (c) 440 (d) 220
4. 4.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 8 (b) 5 (c) 7 (d) 6
5. 5.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 441 (c) 231 (d) 462
6. 6.Which term of the AP 16, 20, 24, 28, … is 48? (a) 10th (b) 9th (c) 8th (d) 12th
7. 7.What is the missing term in the AP 17, 24, ?, 38, 45? (a) 31 (b) 38 (c) 30 (d) 32
8. 8.What is the missing term in the AP 9, ?, 27, 36, 45? (a) 27 (b) 18 (c) 17 (d) 19
9. 9.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 162 (b) 306 (c) 25 (d) 153
10. 10.What is the 29th term of the AP 15, 23, 31, 39, …? (a) 247 (b) 224 (c) 239 (d) 232
11. 11.What is the sum of all the whole numbers from 1 to 80? (a) 3200 (b) 6480 (c) 3240 (d) 3160
12. 12.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 252 (b) 126 (c) 129 (d) 27
13. 13.Which term of the AP 14, 16, 18, 20, … is 62? (a) 26th (b) 24th (c) 31st (d) 25th
14. 14.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 96 (b) 174 (c) 87 (d) 22
15. 15.What is the missing term in the AP 19, 27, ?, 43, 51? (a) 35 (b) 36 (c) 43 (d) 34
16. 16.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 35 (b) 36 (c) 70 (d) 8
17. 17.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 39 (b) 210 (c) 420 (d) 230
18. 18.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5000 (c) 5050 (d) 10100
19. 19.Which term of the AP 9, 11, 13, 15, … is 35? (a) 14th (b) 13th (c) 16th (d) 15th
20. 20.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 1129 (c) 2256 (d) 1128
21. 21.What is the missing term in the AP 10, 16, 22, ?, 34? (a) 29 (b) 28 (c) 34 (d) 27
22. 22.What is the missing term in the AP 1, 7, ?, 19, 25? (a) 14 (b) 13 (c) 12 (d) 19
23. 23.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 26 (b) 160 (c) 85 (d) 80
24. 24.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 90 (b) 17 (c) 162 (d) 81
25. 25.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 8372 (c) 4186 (d) 4095
26. 26.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 114 (b) 27 (c) 204 (d) 102
27. 27.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 552 (c) 529 (d) 45
28. 28.What is the sum of all the whole numbers from 1 to 30? (a) 435 (b) 450 (c) 930 (d) 465
29. 29.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 19 (b) 290 (c) 150 (d) 145
30. 30.What is the 14th term of the AP 17, 20, 23, 26, …? (a) 42 (b) 59 (c) 39 (d) 56
31. 31.Which term of the AP 17, 22, 27, 32, … is 127? (a) 25th (b) 23rd (c) 24th (d) 22nd
32. 32.What is the sum of all the whole numbers from 1 to 98? (a) 4753 (b) 4802 (c) 4851 (d) 9702
33. 33.Which term of the AP 20, 23, 26, 29, … is 47? (a) 9th (b) 12th (c) 11th (d) 10th
34. 34.What is the missing term in the AP 5, ?, 19, 26, 33? (a) 12 (b) 13 (c) 11 (d) 19
35. 35.Which term of the AP 14, 20, 26, 32, … is 230? (a) 39th (b) 38th (c) 37th (d) 36th
36. 36.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 255 (b) 280 (c) 48 (d) 510
37. 37.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 36 (d) 64
38. 38.Which term of the AP 20, 26, 32, 38, … is 116? (a) 17th (b) 19th (c) 16th (d) 18th
39. 39.What is the missing term in the AP 20, 27, 34, ?, 48? (a) 48 (b) 40 (c) 41 (d) 42
40. 40.What is the sum of all the whole numbers from 1 to 32? (a) 496 (b) 528 (c) 1056 (d) 512

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