Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 495 · 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 13, ?, 29, 37, 45? (a) 20 (b) 22 (c) 21 (d) 29
2. 2.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 3240 (c) 6642 (d) 3321
3. 3.Which term of the AP 17, 21, 25, 29, … is 85? (a) 19th (b) 17th (c) 20th (d) 18th
4. 4.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 14 (b) 69 (c) 72 (d) 138
5. 5.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 30 (d) 15
6. 6.What is the 33rd term of the AP 19, 22, 25, 28, …? (a) 118 (b) 115 (c) 96 (d) 99
7. 7.Which term of the AP 2, 4, 6, 8, … is 46? (a) 22nd (b) 23rd (c) 24th (d) 25th
8. 8.Which term of the AP 14, 16, 18, 20, … is 50? (a) 19th (b) 18th (c) 25th (d) 20th
9. 9.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 372 (b) 21 (c) 186 (d) 192
10. 10.What is the 32nd term of the AP 1, 3, 5, 7, …? (a) 62 (b) 65 (c) 64 (d) 63
11. 11.What is the missing term in the AP 19, 21, ?, 25, 27? (a) 23 (b) 24 (c) 25 (d) 22
12. 12.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 7 (b) 6 (c) 10 (d) 8
13. 13.What is the 14th term of the AP 13, 16, 19, 22, …? (a) 52 (b) 39 (c) 55 (d) 42
14. 14.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 27 (b) 20 (c) 18 (d) 19
15. 15.What is the 29th term of the AP 20, 28, 36, 44, …? (a) 244 (b) 224 (c) 252 (d) 232
16. 16.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 49 (b) 530 (c) 265 (d) 290
17. 17.What is the 28th term of the AP 4, 6, 8, 10, …? (a) 58 (b) 60 (c) 54 (d) 56
18. 18.What is the missing term in the AP 6, ?, 22, 30, 38? (a) 15 (b) 13 (c) 14 (d) 22
19. 19.What is the missing term in the AP 11, 16, ?, 26, 31? (a) 20 (b) 22 (c) 26 (d) 21
20. 20.What is the 37th term of the AP 11, 18, 25, 32, …? (a) 259 (b) 252 (c) 270 (d) 263
21. 21.Which term of the AP 4, 9, 14, 19, … is 74? (a) 17th (b) 14th (c) 15th (d) 16th
22. 22.What is the missing term in the AP 8, ?, 12, 14, 16? (a) 10 (b) 9 (c) 12 (d) 11
23. 23.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 784 (d) 812
24. 24.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 3 (b) 6 (c) 5 (d) 4
25. 25.What is the 27th term of the AP 4, 11, 18, 25, …? (a) 182 (b) 186 (c) 193 (d) 189
26. 26.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 210 (d) 39
27. 27.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 144 (d) 23
28. 28.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 99 (b) 100 (c) 14 (d) 198
29. 29.Which term of the AP 19, 27, 35, 43, … is 171? (a) 21st (b) 20th (c) 22nd (d) 19th
30. 30.What is the 14th term of the AP 17, 21, 25, 29, …? (a) 56 (b) 73 (c) 52 (d) 69
31. 31.What is the missing term in the AP 14, ?, 20, 23, 26? (a) 20 (b) 18 (c) 17 (d) 16
32. 32.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21
33. 33.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 14 (b) 17 (c) 12 (d) 13
34. 34.What is the 38th term of the AP 2, 5, 8, 11, …? (a) 111 (b) 114 (c) 116 (d) 113
35. 35.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 529 (c) 276 (d) 45
36. 36.What is the sum of all the whole numbers from 1 to 65? (a) 2146 (b) 2080 (c) 2145 (d) 4290
37. 37.What is the 18th term of the AP 10, 16, 22, 28, …? (a) 108 (b) 102 (c) 118 (d) 112
38. 38.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 305 (b) 610 (c) 53 (d) 330
39. 39.What is the missing term in the AP 19, 23, 27, ?, 35? (a) 30 (b) 35 (c) 31 (d) 32
40. 40.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 187 (b) 176 (c) 352 (d) 26

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