Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 64 · 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 23rd term of the AP 14, 22, 30, 38, …? (a) 190 (b) 198 (c) 184 (d) 176
2. 2.What is the missing term in the AP 10, 12, ?, 16, 18? (a) 13 (b) 15 (c) 16 (d) 14
3. 3.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 98 (b) 49 (c) 50 (d) 10
4. 4.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 153 (c) 342 (d) 171
5. 5.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 32 (b) 360 (c) 180 (d) 183
6. 6.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 179 (b) 176 (c) 31 (d) 352
7. 7.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 3192 (c) 1540 (d) 1596
8. 8.What is the missing term in the AP 7, 13, 19, ?, 31? (a) 26 (b) 25 (c) 31 (d) 24
9. 9.What is the 33rd term of the AP 5, 7, 9, 11, …? (a) 69 (b) 71 (c) 64 (d) 66
10. 10.What is the 34th term of the AP 18, 24, 30, 36, …? (a) 198 (b) 216 (c) 222 (d) 204
11. 11.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 168 (b) 147 (c) 294 (d) 39
12. 12.What is the 25th term of the AP 19, 27, 35, 43, …? (a) 200 (b) 219 (c) 192 (d) 211
13. 13.Which term of the AP 15, 18, 21, 24, … is 114? (a) 33rd (b) 38th (c) 35th (d) 34th
14. 14.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 210 (d) 105
15. 15.What is the missing term in the AP 18, 23, 28, ?, 38? (a) 33 (b) 32 (c) 34 (d) 38
16. 16.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 135 (b) 270 (c) 27 (d) 138
17. 17.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 552 (c) 276 (d) 277
18. 18.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 41 (d) 441
19. 19.Which term of the AP 6, 10, 14, 18, … is 126? (a) 31st (b) 30th (c) 32nd (d) 33rd
20. 20.What is the 31st term of the AP 5, 14, 23, 32, …? (a) 279 (b) 270 (c) 275 (d) 284
21. 21.What is the 21st term of the AP 16, 19, 22, 25, …? (a) 79 (b) 60 (c) 63 (d) 76
22. 22.What is the sum of all the whole numbers from 1 to 60? (a) 1770 (b) 1830 (c) 1800 (d) 3660
23. 23.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 14 (b) 11 (c) 10 (d) 12
24. 24.What is the 38th term of the AP 19, 22, 25, 28, …? (a) 111 (b) 133 (c) 114 (d) 130
25. 25.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 666 (c) 630 (d) 648
26. 26.What is the missing term in the AP 5, ?, 17, 23, 29? (a) 10 (b) 12 (c) 11 (d) 17
27. 27.What is the 25th term of the AP 8, 14, 20, 26, …? (a) 152 (b) 150 (c) 144 (d) 158
28. 28.What is the 36th term of the AP 6, 8, 10, 12, …? (a) 76 (b) 72 (c) 70 (d) 78
29. 29.What is the missing term in the AP 16, ?, 26, 31, 36? (a) 21 (b) 22 (c) 20 (d) 26
30. 30.What is the 18th term of the AP 19, 27, 35, 43, …? (a) 136 (b) 163 (c) 144 (d) 155
31. 31.What is the 36th term of the AP 2, 4, 6, 8, …? (a) 70 (b) 72 (c) 74 (d) 73
32. 32.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 6 (b) 4 (c) 5 (d) 7
33. 33.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2628 (c) 2592 (d) 2556
34. 34.What is the sum of all the whole numbers from 1 to 32? (a) 528 (b) 496 (c) 512 (d) 1056
35. 35.What is the 33rd term of the AP 2, 5, 8, 11, …? (a) 99 (b) 96 (c) 98 (d) 101
36. 36.What is the missing term in the AP 17, 20, 23, ?, 29? (a) 25 (b) 27 (c) 26 (d) 29
37. 37.What is the 10th term of the AP 15, 17, 19, 21, …? (a) 18 (b) 35 (c) 20 (d) 33
38. 38.What is the 37th term of the AP 20, 26, 32, 38, …? (a) 242 (b) 236 (c) 216 (d) 222
39. 39.What is the missing term in the AP 17, ?, 23, 26, 29? (a) 19 (b) 23 (c) 20 (d) 21
40. 40.What is the 12th term of the AP 10, 17, 24, 31, …? (a) 84 (b) 87 (c) 77 (d) 94

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