Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 164 · 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 8 terms of the AP 4, 9, 14, …? (a) 344 (b) 39 (c) 192 (d) 172
2. 2.What is the 35th term of the AP 12, 16, 20, 24, …? (a) 140 (b) 152 (c) 148 (d) 136
3. 3.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 13 (b) 12 (c) 11 (d) 18
4. 4.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 45 (d) 529
5. 5.What is the 36th term of the AP 3, 12, 21, 30, …? (a) 327 (b) 324 (c) 318 (d) 315
6. 6.What is the 15th term of the AP 19, 27, 35, 43, …? (a) 131 (b) 112 (c) 120 (d) 139
7. 7.What is the 15th term of the AP 4, 6, 8, 10, …? (a) 34 (b) 28 (c) 30 (d) 32
8. 8.What is the 13th term of the AP 1, 3, 5, 7, …? (a) 24 (b) 25 (c) 27 (d) 26
9. 9.What is the 21st term of the AP 4, 8, 12, 16, …? (a) 80 (b) 85 (c) 84 (d) 88
10. 10.What is the 18th term of the AP 15, 21, 27, 33, …? (a) 123 (b) 117 (c) 108 (d) 102
11. 11.Which term of the AP 20, 23, 26, 29, … is 104? (a) 28th (b) 29th (c) 30th (d) 31st
12. 12.Which term of the AP 13, 17, 21, 25, … is 149? (a) 34th (b) 35th (c) 37th (d) 36th
13. 13.Which term of the AP 3, 9, 15, 21, … is 171? (a) 30th (b) 31st (c) 28th (d) 29th
14. 14.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 256 (b) 30 (c) 144 (d) 128
15. 15.Which term of the AP 2, 4, 6, 8, … is 44? (a) 23rd (b) 22nd (c) 21st (d) 24th
16. 16.What is the 25th term of the AP 7, 13, 19, 25, …? (a) 157 (b) 150 (c) 144 (d) 151
17. 17.What is the 21st term of the AP 16, 19, 22, 25, …? (a) 60 (b) 76 (c) 79 (d) 63
18. 18.What is the 16th term of the AP 14, 23, 32, 41, …? (a) 149 (b) 135 (c) 144 (d) 158
19. 19.What is the missing term in the AP 7, 11, 15, ?, 23? (a) 18 (b) 23 (c) 19 (d) 20
20. 20.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 9506 (c) 4753 (d) 4656
21. 21.What is the 17th term of the AP 12, 15, 18, 21, …? (a) 48 (b) 63 (c) 60 (d) 51
22. 22.What is the 37th term of the AP 3, 10, 17, 24, …? (a) 252 (b) 259 (c) 255 (d) 262
23. 23.What is the 29th term of the AP 4, 6, 8, 10, …? (a) 62 (b) 58 (c) 60 (d) 56
24. 24.What is the 36th term of the AP 2, 6, 10, 14, …? (a) 144 (b) 142 (c) 146 (d) 140
25. 25.What is the 21st term of the AP 15, 21, 27, 33, …? (a) 126 (b) 141 (c) 135 (d) 120
26. 26.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 108 (b) 14 (c) 102 (d) 204
27. 27.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 23 (b) 156 (c) 78 (d) 90
28. 28.What is the 19th term of the AP 9, 14, 19, 24, …? (a) 90 (b) 104 (c) 99 (d) 95
29. 29.What is the 10th term of the AP 6, 12, 18, 24, …? (a) 66 (b) 60 (c) 61 (d) 54
30. 30.What is the 40th term of the AP 7, 13, 19, 25, …? (a) 240 (b) 247 (c) 241 (d) 234
31. 31.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 22 (b) 264 (c) 143 (d) 132
32. 32.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 90 (b) 50 (c) 13 (d) 45
33. 33.Which term of the AP 15, 24, 33, 42, … is 141? (a) 16th (b) 14th (c) 15th (d) 17th
34. 34.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 576 (c) 47 (d) 300
35. 35.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 300 (c) 325 (d) 326
36. 36.What is the sum of all the whole numbers from 1 to 32? (a) 496 (b) 512 (c) 1056 (d) 528
37. 37.What is the missing term in the AP 15, 19, 23, ?, 31? (a) 26 (b) 28 (c) 27 (d) 31
38. 38.What is the 11th term of the AP 9, 11, 13, 15, …? (a) 31 (b) 20 (c) 22 (d) 29
39. 39.What is the 17th term of the AP 10, 12, 14, 16, …? (a) 34 (b) 44 (c) 42 (d) 32
40. 40.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 201 (b) 396 (c) 34 (d) 198

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