Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 274 · 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 6 terms of the AP 4, 10, 16, …? (a) 34 (b) 132 (c) 114 (d) 228
2. 2.What is the 21st term of the AP 6, 11, 16, 21, …? (a) 111 (b) 106 (c) 105 (d) 100
3. 3.What is the 13th term of the AP 8, 15, 22, 29, …? (a) 91 (b) 99 (c) 84 (d) 92
4. 4.What is the 11th term of the AP 5, 7, 9, 11, …? (a) 20 (b) 22 (c) 25 (d) 27
5. 5.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 361 (c) 380 (d) 190
6. 6.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 66 (d) 121
7. 7.What is the missing term in the AP 20, ?, 38, 47, 56? (a) 28 (b) 29 (c) 30 (d) 38
8. 8.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 435 (c) 870 (d) 57
9. 9.What is the 16th term of the AP 7, 11, 15, 19, …? (a) 60 (b) 67 (c) 71 (d) 64
10. 10.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 20 (b) 22 (c) 21 (d) 28
11. 11.What is the 22nd term of the AP 7, 13, 19, 25, …? (a) 126 (b) 139 (c) 133 (d) 132
12. 12.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 64 (b) 120 (c) 60 (d) 11
13. 13.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 342 (c) 171 (d) 324
14. 14.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 9 (c) 30 (d) 15
15. 15.What is the missing term in the AP 8, 16, ?, 32, 40? (a) 25 (b) 24 (c) 23 (d) 32
16. 16.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 43 (c) 253 (d) 506
17. 17.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 29 (b) 418 (c) 209 (d) 220
18. 18.What is the 33rd term of the AP 12, 14, 16, 18, …? (a) 78 (b) 66 (c) 76 (d) 64
19. 19.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 2416 (c) 4830 (d) 2415
20. 20.What is the sum of all the whole numbers from 1 to 37? (a) 704 (b) 703 (c) 1406 (d) 666
21. 21.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 72 (b) 64 (c) 128 (d) 15
22. 22.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 85 (b) 70 (c) 140 (d) 26
23. 23.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 812 (c) 406 (d) 55
24. 24.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 1653 (c) 1711 (d) 3422
25. 25.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 172 (b) 344 (c) 192 (d) 39
26. 26.What is the 26th term of the AP 17, 23, 29, 35, …? (a) 173 (b) 150 (c) 167 (d) 156
27. 27.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 900 (c) 59 (d) 465
28. 28.What is the missing term in the AP 3, ?, 19, 27, 35? (a) 11 (b) 12 (c) 10 (d) 19
29. 29.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
30. 30.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 441 (d) 41
31. 31.What is the 12th term of the AP 4, 8, 12, 16, …? (a) 44 (b) 52 (c) 48 (d) 49
32. 32.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 946 (c) 1980 (d) 968
33. 33.What is the missing term in the AP 11, 19, ?, 35, 43? (a) 35 (b) 26 (c) 28 (d) 27
34. 34.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 10100 (c) 5000 (d) 5050
35. 35.What is the 36th term of the AP 2, 7, 12, 17, …? (a) 177 (b) 180 (c) 182 (d) 175
36. 36.What is the 24th term of the AP 20, 26, 32, 38, …? (a) 144 (b) 138 (c) 158 (d) 164
37. 37.Which term of the AP 5, 14, 23, 32, … is 248? (a) 27th (b) 28th (c) 29th (d) 30th
38. 38.What is the sum of the first 10 terms of the AP 7, 10, 13, …? (a) 34 (b) 205 (c) 410 (d) 220
39. 39.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 136 (c) 256 (d) 31
40. 40.What is the 18th term of the AP 4, 6, 8, 10, …? (a) 36 (b) 40 (c) 38 (d) 34

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