Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 185 · 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 all the whole numbers from 1 to 17? (a) 153 (b) 154 (c) 136 (d) 306
2. 2.What is the missing term in the AP 7, 14, 21, ?, 35? (a) 27 (b) 28 (c) 35 (d) 29
3. 3.Which term of the AP 16, 18, 20, 22, … is 64? (a) 26th (b) 25th (c) 32nd (d) 24th
4. 4.What is the sum of the first 9 terms of the AP 4, 6, 8, …? (a) 216 (b) 20 (c) 108 (d) 117
5. 5.What is the 18th term of the AP 3, 11, 19, 27, …? (a) 139 (b) 147 (c) 136 (d) 144
6. 6.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 45 (c) 552 (d) 276
7. 7.Which term of the AP 12, 14, 16, 18, … is 50? (a) 21st (b) 20th (c) 19th (d) 25th
8. 8.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 253 (c) 506 (d) 484
9. 9.Which term of the AP 16, 25, 34, 43, … is 133? (a) 16th (b) 15th (c) 14th (d) 13th
10. 10.Which term of the AP 9, 17, 25, 33, … is 65? (a) 7th (b) 9th (c) 8th (d) 10th
11. 11.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 594 (b) 302 (c) 297 (d) 52
12. 12.Which term of the AP 8, 15, 22, 29, … is 267? (a) 38th (b) 39th (c) 37th (d) 40th
13. 13.What is the sum of all the whole numbers from 1 to 45? (a) 1035 (b) 1036 (c) 2070 (d) 990
14. 14.What is the missing term in the AP 20, ?, 32, 38, 44? (a) 26 (b) 32 (c) 27 (d) 25
15. 15.What is the sum of the first 6 terms of the AP 1, 4, 7, …? (a) 51 (b) 102 (c) 60 (d) 16
16. 16.What is the 10th term of the AP 14, 18, 22, 26, …? (a) 40 (b) 50 (c) 36 (d) 54
17. 17.What is the sum of all the whole numbers from 1 to 68? (a) 2312 (b) 2346 (c) 4692 (d) 2278
18. 18.What is the 15th term of the AP 13, 19, 25, 31, …? (a) 84 (b) 103 (c) 90 (d) 97
19. 19.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 156 (d) 144
20. 20.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 192 (b) 45 (c) 384 (d) 216
21. 21.What is the missing term in the AP 14, 16, ?, 20, 22? (a) 20 (b) 17 (c) 19 (d) 18
22. 22.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 184 (b) 92 (c) 96 (d) 15
23. 23.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 812 (d) 406
24. 24.What is the 32nd term of the AP 4, 9, 14, 19, …? (a) 159 (b) 160 (c) 155 (d) 164
25. 25.Which term of the AP 20, 25, 30, 35, … is 160? (a) 29th (b) 32nd (c) 28th (d) 30th
26. 26.What is the 27th term of the AP 18, 24, 30, 36, …? (a) 162 (b) 156 (c) 180 (d) 174
27. 27.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 4851 (c) 9702 (d) 4753
28. 28.What is the 17th term of the AP 20, 24, 28, 32, …? (a) 64 (b) 68 (c) 88 (d) 84
29. 29.Which term of the AP 8, 11, 14, 17, … is 95? (a) 31st (b) 30th (c) 32nd (d) 29th
30. 30.What is the missing term in the AP 20, 28, ?, 44, 52? (a) 35 (b) 44 (c) 36 (d) 37
31. 31.What is the 40th term of the AP 8, 12, 16, 20, …? (a) 160 (b) 168 (c) 164 (d) 156
32. 32.What is the 27th term of the AP 13, 20, 27, 34, …? (a) 202 (b) 182 (c) 189 (d) 195
33. 33.What is the 26th term of the AP 12, 20, 28, 36, …? (a) 200 (b) 220 (c) 208 (d) 212
34. 34.What is the 18th term of the AP 13, 16, 19, 22, …? (a) 64 (b) 51 (c) 67 (d) 54
35. 35.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 63 (b) 18 (c) 120 (d) 60
36. 36.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 378 (b) 189 (c) 33 (d) 192
37. 37.What is the missing term in the AP 9, 13, 17, ?, 25? (a) 25 (b) 20 (c) 21 (d) 22
38. 38.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 82 (b) 81 (c) 13 (d) 162
39. 39.What is the 21st term of the AP 20, 22, 24, 26, …? (a) 60 (b) 62 (c) 42 (d) 40
40. 40.What is the sum of all the whole numbers from 1 to 37? (a) 703 (b) 1406 (c) 666 (d) 704

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