Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 339 · 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 missing term in the AP 17, ?, 33, 41, 49? (a) 33 (b) 26 (c) 24 (d) 25
2. 2.What is the 13th term of the AP 19, 25, 31, 37, …? (a) 72 (b) 78 (c) 97 (d) 91
3. 3.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 242 (b) 121 (c) 16 (d) 122
4. 4.What is the 16th term of the AP 7, 13, 19, 25, …? (a) 96 (b) 97 (c) 103 (d) 90
5. 5.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 2450 (c) 1226 (d) 1176
6. 6.What is the 31st term of the AP 3, 12, 21, 30, …? (a) 279 (b) 270 (c) 273 (d) 282
7. 7.What is the 20th term of the AP 16, 24, 32, 40, …? (a) 168 (b) 160 (c) 176 (d) 152
8. 8.What is the 24th term of the AP 17, 22, 27, 32, …? (a) 115 (b) 137 (c) 132 (d) 120
9. 9.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 322 (b) 41 (c) 161 (d) 182
10. 10.What is the 30th term of the AP 7, 9, 11, 13, …? (a) 60 (b) 65 (c) 67 (d) 58
11. 11.What is the 32nd term of the AP 5, 14, 23, 32, …? (a) 293 (b) 279 (c) 288 (d) 284
12. 12.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 78 (d) 91
13. 13.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 252 (b) 480 (c) 31 (d) 240
14. 14.What is the 13th term of the AP 1, 6, 11, 16, …? (a) 60 (b) 65 (c) 61 (d) 66
15. 15.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 3322 (c) 6642 (d) 3321
16. 16.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 35 (b) 40 (c) 70 (d) 11
17. 17.Which term of the AP 3, 9, 15, 21, … is 237? (a) 42nd (b) 39th (c) 41st (d) 40th
18. 18.What is the 13th term of the AP 1, 9, 17, 25, …? (a) 104 (b) 105 (c) 96 (d) 97
19. 19.Which term of the AP 8, 16, 24, 32, … is 104? (a) 12th (b) 13th (c) 15th (d) 14th
20. 20.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 756 (c) 378 (d) 379
21. 21.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 392 (c) 406 (d) 378
22. 22.What is the missing term in the AP 16, 21, 26, ?, 36? (a) 32 (b) 30 (c) 36 (d) 31
23. 23.Which term of the AP 7, 12, 17, 22, … is 182? (a) 36th (b) 35th (c) 37th (d) 38th
24. 24.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 17 (b) 19 (c) 22 (d) 18
25. 25.What is the missing term in the AP 10, ?, 18, 22, 26? (a) 13 (b) 14 (c) 18 (d) 15
26. 26.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 36 (d) 72
27. 27.What is the 40th term of the AP 2, 4, 6, 8, …? (a) 78 (b) 81 (c) 80 (d) 82
28. 28.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 12 (b) 51 (c) 100 (d) 50
29. 29.What is the 25th term of the AP 1, 6, 11, 16, …? (a) 125 (b) 126 (c) 120 (d) 121
30. 30.What is the 15th term of the AP 1, 4, 7, 10, …? (a) 43 (b) 46 (c) 42 (d) 45
31. 31.What is the 20th term of the AP 17, 19, 21, 23, …? (a) 40 (b) 55 (c) 57 (d) 38
32. 32.What is the 10th term of the AP 19, 28, 37, 46, …? (a) 100 (b) 90 (c) 109 (d) 81
33. 33.What is the 33rd term of the AP 4, 7, 10, 13, …? (a) 99 (b) 100 (c) 103 (d) 96
34. 34.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 294 (b) 168 (c) 147 (d) 39
35. 35.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 7 (b) 26 (c) 25 (d) 50
36. 36.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 154 (b) 308 (c) 165 (d) 24
37. 37.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 3160 (c) 6320 (d) 3081
38. 38.What is the 12th term of the AP 9, 14, 19, 24, …? (a) 55 (b) 64 (c) 69 (d) 60
39. 39.What is the 22nd term of the AP 8, 13, 18, 23, …? (a) 110 (b) 118 (c) 113 (d) 105
40. 40.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 13 (b) 12 (c) 11 (d) 10

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