Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 571 · 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 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 253 (d) 484
2. 2.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 6320 (c) 3160 (d) 3081
3. 3.What is the 37th term of the AP 11, 20, 29, 38, …? (a) 344 (b) 324 (c) 335 (d) 333
4. 4.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 784 (c) 55 (d) 812
5. 5.What is the missing term in the AP 16, ?, 22, 25, 28? (a) 22 (b) 18 (c) 20 (d) 19
6. 6.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 140 (b) 280 (c) 38 (d) 161
7. 7.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 54 (b) 60 (c) 108 (d) 14
8. 8.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 99 (b) 198 (c) 15 (d) 100
9. 9.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 2851 (c) 5700 (d) 2850
10. 10.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 130 (b) 65 (c) 75 (d) 21
11. 11.What is the 21st term of the AP 8, 17, 26, 35, …? (a) 197 (b) 180 (c) 189 (d) 188
12. 12.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 169 (d) 25
13. 13.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 732 (b) 396 (c) 366 (d) 58
14. 14.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 900 (c) 930 (d) 59
15. 15.What is the 26th term of the AP 8, 15, 22, 29, …? (a) 190 (b) 175 (c) 182 (d) 183
16. 16.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 562 (c) 561 (d) 1122
17. 17.What is the 11th term of the AP 8, 11, 14, 17, …? (a) 30 (b) 33 (c) 41 (d) 38
18. 18.What is the 18th term of the AP 4, 7, 10, 13, …? (a) 58 (b) 55 (c) 51 (d) 54
19. 19.What is the 12th term of the AP 9, 11, 13, 15, …? (a) 24 (b) 31 (c) 22 (d) 33
20. 20.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 520 (b) 260 (c) 280 (d) 44
21. 21.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 164 (b) 38 (c) 328 (d) 184
22. 22.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1226 (c) 1225 (d) 1176
23. 23.What is the missing term in the AP 13, ?, 31, 40, 49? (a) 21 (b) 31 (c) 23 (d) 22
24. 24.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 650 (c) 625 (d) 325
25. 25.Which term of the AP 7, 13, 19, 25, … is 199? (a) 34th (b) 35th (c) 32nd (d) 33rd
26. 26.What is the 13th term of the AP 16, 24, 32, 40, …? (a) 96 (b) 120 (c) 112 (d) 104
27. 27.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 66 (b) 114 (c) 57 (d) 17
28. 28.What is the 13th term of the AP 14, 22, 30, 38, …? (a) 110 (b) 96 (c) 118 (d) 104
29. 29.Which term of the AP 15, 23, 31, 39, … is 183? (a) 24th (b) 23rd (c) 21st (d) 22nd
30. 30.What is the missing term in the AP 12, ?, 28, 36, 44? (a) 20 (b) 19 (c) 21 (d) 28
31. 31.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 2256 (c) 1128 (d) 1081
32. 32.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 201 (b) 396 (c) 198 (d) 33
33. 33.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 126 (b) 252 (c) 129 (d) 26
34. 34.What is the 29th term of the AP 14, 18, 22, 26, …? (a) 130 (b) 116 (c) 126 (d) 112
35. 35.Which term of the AP 11, 20, 29, 38, … is 326? (a) 37th (b) 38th (c) 35th (d) 36th
36. 36.What is the missing term in the AP 7, ?, 17, 22, 27? (a) 11 (b) 17 (c) 13 (d) 12
37. 37.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 124 (b) 119 (c) 238 (d) 32
38. 38.What is the missing term in the AP 5, ?, 13, 17, 21? (a) 10 (b) 8 (c) 13 (d) 9
39. 39.What is the 32nd term of the AP 9, 11, 13, 15, …? (a) 71 (b) 64 (c) 62 (d) 73
40. 40.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 870 (c) 57 (d) 841

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