Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 557 · 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 36th term of the AP 7, 15, 23, 31, …? (a) 295 (b) 287 (c) 280 (d) 288
2. 2.What is the 33rd term of the AP 18, 24, 30, 36, …? (a) 192 (b) 216 (c) 210 (d) 198
3. 3.What is the missing term in the AP 7, ?, 11, 13, 15? (a) 9 (b) 8 (c) 10 (d) 11
4. 4.What is the 30th term of the AP 2, 5, 8, 11, …? (a) 90 (b) 89 (c) 87 (d) 92
5. 5.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4753 (c) 4851 (d) 4802
6. 6.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 66 (c) 55 (d) 67
7. 7.What is the 17th term of the AP 16, 25, 34, 43, …? (a) 153 (b) 169 (c) 144 (d) 160
8. 8.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 361 (d) 380
9. 9.What is the 19th term of the AP 6, 11, 16, 21, …? (a) 96 (b) 101 (c) 95 (d) 90
10. 10.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 392 (c) 406 (d) 378
11. 11.Which term of the AP 10, 16, 22, 28, … is 52? (a) 8th (b) 7th (c) 9th (d) 10th
12. 12.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 132 (b) 67 (c) 11 (d) 66
13. 13.What is the sum of all the whole numbers from 1 to 24? (a) 300 (b) 276 (c) 600 (d) 288
14. 14.What is the 27th term of the AP 1, 6, 11, 16, …? (a) 130 (b) 131 (c) 136 (d) 135
15. 15.Which term of the AP 1, 4, 7, 10, … is 85? (a) 31st (b) 29th (c) 30th (d) 28th
16. 16.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 552 (c) 277 (d) 276
17. 17.What is the missing term in the AP 13, ?, 31, 40, 49? (a) 31 (b) 21 (c) 22 (d) 23
18. 18.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 33 (d) 289
19. 19.What is the missing term in the AP 18, 23, 28, ?, 38? (a) 38 (b) 34 (c) 32 (d) 33
20. 20.Which term of the AP 14, 17, 20, 23, … is 86? (a) 27th (b) 24th (c) 26th (d) 25th
21. 21.What is the 12th term of the AP 7, 12, 17, 22, …? (a) 55 (b) 60 (c) 62 (d) 67
22. 22.What is the missing term in the AP 14, 20, ?, 32, 38? (a) 25 (b) 32 (c) 26 (d) 27
23. 23.What is the 40th term of the AP 17, 19, 21, 23, …? (a) 95 (b) 80 (c) 78 (d) 97
24. 24.What is the missing term in the AP 13, 17, 21, ?, 29? (a) 25 (b) 24 (c) 26 (d) 29
25. 25.What is the 18th term of the AP 7, 15, 23, 31, …? (a) 151 (b) 136 (c) 144 (d) 143
26. 26.What is the missing term in the AP 16, 21, ?, 31, 36? (a) 25 (b) 26 (c) 31 (d) 27
27. 27.What is the missing term in the AP 5, 10, 15, ?, 25? (a) 20 (b) 25 (c) 19 (d) 21
28. 28.What is the 10th term of the AP 11, 13, 15, 17, …? (a) 18 (b) 31 (c) 20 (d) 29
29. 29.What is the sum of all the whole numbers from 1 to 90? (a) 4005 (b) 4095 (c) 8190 (d) 4050
30. 30.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 11 (b) 16 (c) 12 (d) 13
31. 31.What is the 15th term of the AP 4, 12, 20, 28, …? (a) 112 (b) 120 (c) 124 (d) 116
32. 32.What is the 12th term of the AP 11, 14, 17, 20, …? (a) 47 (b) 36 (c) 44 (d) 33
33. 33.What is the missing term in the AP 17, 22, ?, 32, 37? (a) 26 (b) 32 (c) 28 (d) 27
34. 34.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 2070 (c) 990 (d) 1035
35. 35.What is the missing term in the AP 3, ?, 11, 15, 19? (a) 8 (b) 7 (c) 6 (d) 11
36. 36.Which term of the AP 4, 10, 16, 22, … is 178? (a) 29th (b) 30th (c) 32nd (d) 31st
37. 37.What is the 37th term of the AP 16, 23, 30, 37, …? (a) 252 (b) 259 (c) 275 (d) 268
38. 38.What is the 22nd term of the AP 11, 13, 15, 17, …? (a) 53 (b) 55 (c) 44 (d) 42
39. 39.What is the 27th term of the AP 7, 16, 25, 34, …? (a) 234 (b) 250 (c) 243 (d) 241
40. 40.Which term of the AP 20, 22, 24, 26, … is 66? (a) 33rd (b) 25th (c) 24th (d) 23rd

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