Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 516 · 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 all the whole numbers from 1 to 71? (a) 2485 (b) 2557 (c) 2556 (d) 5112
2. 2.What is the 36th term of the AP 2, 6, 10, 14, …? (a) 140 (b) 144 (c) 142 (d) 146
3. 3.What is the 25th term of the AP 4, 8, 12, 16, …? (a) 100 (b) 104 (c) 96 (d) 101
4. 4.What is the 32nd term of the AP 3, 12, 21, 30, …? (a) 288 (b) 279 (c) 282 (d) 291
5. 5.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 70 (b) 38 (c) 35 (d) 13
6. 6.Which term of the AP 9, 12, 15, 18, … is 126? (a) 42nd (b) 40th (c) 41st (d) 39th
7. 7.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 9 (d) 25
8. 8.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 210 (b) 105 (c) 114 (d) 25
9. 9.What is the 32nd term of the AP 2, 11, 20, 29, …? (a) 288 (b) 279 (c) 281 (d) 290
10. 10.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 441 (d) 231
11. 11.What is the 31st term of the AP 14, 20, 26, 32, …? (a) 186 (b) 200 (c) 180 (d) 194
12. 12.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 45 (d) 81
13. 13.What is the 10th term of the AP 20, 28, 36, 44, …? (a) 72 (b) 100 (c) 80 (d) 92
14. 14.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 351 (c) 676 (d) 51
15. 15.What is the missing term in the AP 7, 16, ?, 34, 43? (a) 34 (b) 26 (c) 25 (d) 24
16. 16.What is the missing term in the AP 16, 19, 22, ?, 28? (a) 24 (b) 26 (c) 28 (d) 25
17. 17.What is the sum of all the whole numbers from 1 to 80? (a) 3200 (b) 3240 (c) 3160 (d) 6480
18. 18.What is the 22nd term of the AP 16, 20, 24, 28, …? (a) 100 (b) 104 (c) 84 (d) 88
19. 19.What is the 38th term of the AP 5, 10, 15, 20, …? (a) 190 (b) 195 (c) 185 (d) 191
20. 20.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 8 (b) 7 (c) 6 (d) 9
21. 21.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 368 (b) 44 (c) 184 (d) 208
22. 22.What is the missing term in the AP 10, 14, 18, ?, 26? (a) 26 (b) 23 (c) 21 (d) 22
23. 23.What is the 17th term of the AP 9, 14, 19, 24, …? (a) 94 (b) 80 (c) 85 (d) 89
24. 24.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 105 (d) 210
25. 25.What is the 37th term of the AP 6, 9, 12, 15, …? (a) 117 (b) 108 (c) 111 (d) 114
26. 26.What is the 35th term of the AP 2, 4, 6, 8, …? (a) 70 (b) 72 (c) 71 (d) 68
27. 27.What is the missing term in the AP 5, ?, 11, 14, 17? (a) 11 (b) 9 (c) 8 (d) 7
28. 28.What is the 27th term of the AP 10, 12, 14, 16, …? (a) 54 (b) 64 (c) 62 (d) 52
29. 29.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 11 (b) 12 (c) 10 (d) 13
30. 30.Which term of the AP 1, 3, 5, 7, … is 63? (a) 32nd (b) 34th (c) 33rd (d) 31st
31. 31.What is the missing term in the AP 20, 28, ?, 44, 52? (a) 37 (b) 35 (c) 36 (d) 44
32. 32.What is the missing term in the AP 10, 12, 14, ?, 18? (a) 15 (b) 17 (c) 18 (d) 16
33. 33.Which term of the AP 15, 23, 31, 39, … is 319? (a) 38th (b) 40th (c) 39th (d) 41st
34. 34.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 378 (c) 812 (d) 406
35. 35.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 21 (d) 42
36. 36.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 2080 (c) 4160 (d) 2016
37. 37.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 120 (b) 15 (c) 114 (d) 228
38. 38.What is the missing term in the AP 3, ?, 19, 27, 35? (a) 10 (b) 11 (c) 19 (d) 12
39. 39.What is the 10th term of the AP 12, 14, 16, 18, …? (a) 20 (b) 18 (c) 32 (d) 30
40. 40.What is the missing term in the AP 2, 6, 10, ?, 18? (a) 14 (b) 15 (c) 18 (d) 13

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