Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 179 · 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 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 132 (d) 121
2. 2.Which term of the AP 15, 19, 23, 27, … is 127? (a) 28th (b) 29th (c) 31st (d) 30th
3. 3.Which term of the AP 6, 15, 24, 33, … is 357? (a) 41st (b) 40th (c) 39th (d) 42nd
4. 4.What is the 28th term of the AP 10, 15, 20, 25, …? (a) 140 (b) 150 (c) 145 (d) 135
5. 5.What is the 20th term of the AP 15, 20, 25, 30, …? (a) 95 (b) 115 (c) 100 (d) 110
6. 6.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 34 (b) 420 (c) 228 (d) 210
7. 7.What is the 14th term of the AP 4, 8, 12, 16, …? (a) 52 (b) 60 (c) 57 (d) 56
8. 8.What is the 35th term of the AP 6, 14, 22, 30, …? (a) 286 (b) 280 (c) 272 (d) 278
9. 9.What is the sum of the first 8 terms of the AP 6, 11, 16, …? (a) 376 (b) 41 (c) 208 (d) 188
10. 10.What is the missing term in the AP 18, 23, ?, 33, 38? (a) 33 (b) 27 (c) 29 (d) 28
11. 11.What is the 12th term of the AP 3, 5, 7, 9, …? (a) 27 (b) 25 (c) 22 (d) 24
12. 12.What is the 22nd term of the AP 18, 23, 28, 33, …? (a) 123 (b) 128 (c) 105 (d) 110
13. 13.What is the 21st term of the AP 12, 14, 16, 18, …? (a) 54 (b) 40 (c) 52 (d) 42
14. 14.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 702 (d) 676
15. 15.What is the 40th term of the AP 10, 18, 26, 34, …? (a) 320 (b) 312 (c) 322 (d) 330
16. 16.Which term of the AP 15, 24, 33, 42, … is 303? (a) 34th (b) 35th (c) 32nd (d) 33rd
17. 17.What is the 10th term of the AP 20, 25, 30, 35, …? (a) 70 (b) 50 (c) 45 (d) 65
18. 18.What is the 25th term of the AP 4, 9, 14, 19, …? (a) 125 (b) 120 (c) 129 (d) 124
19. 19.What is the 10th term of the AP 4, 12, 20, 28, …? (a) 72 (b) 84 (c) 80 (d) 76
20. 20.Which term of the AP 10, 12, 14, 16, … is 76? (a) 35th (b) 38th (c) 34th (d) 33rd
21. 21.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 196 (d) 27
22. 22.What is the 40th term of the AP 6, 15, 24, 33, …? (a) 357 (b) 360 (c) 351 (d) 366
23. 23.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 35 (b) 36 (c) 70 (d) 8
24. 24.What is the 11th term of the AP 19, 28, 37, 46, …? (a) 118 (b) 90 (c) 99 (d) 109
25. 25.What is the missing term in the AP 9, 13, ?, 21, 25? (a) 16 (b) 21 (c) 18 (d) 17
26. 26.What is the 18th term of the AP 16, 19, 22, 25, …? (a) 67 (b) 51 (c) 54 (d) 70
27. 27.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1485 (c) 1431 (d) 2970
28. 28.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 48 (b) 13 (c) 54 (d) 96
29. 29.What is the 10th term of the AP 15, 20, 25, 30, …? (a) 45 (b) 50 (c) 60 (d) 65
30. 30.What is the missing term in the AP 1, 5, 9, ?, 17? (a) 12 (b) 13 (c) 17 (d) 14
31. 31.What is the missing term in the AP 11, 20, 29, ?, 47? (a) 39 (b) 47 (c) 37 (d) 38
32. 32.What is the sum of all the whole numbers from 1 to 60? (a) 1830 (b) 1800 (c) 3660 (d) 1770
33. 33.Which term of the AP 7, 10, 13, 16, … is 109? (a) 36th (b) 35th (c) 37th (d) 34th
34. 34.What is the missing term in the AP 20, 25, ?, 35, 40? (a) 30 (b) 29 (c) 31 (d) 35
35. 35.What is the 39th term of the AP 11, 14, 17, 20, …? (a) 125 (b) 117 (c) 128 (d) 114
36. 36.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 9 (b) 84 (c) 43 (d) 42
37. 37.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 4160 (c) 2080 (d) 2048
38. 38.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 16 (b) 104 (c) 200 (d) 100
39. 39.What is the sum of all the whole numbers from 1 to 17? (a) 154 (b) 153 (c) 136 (d) 306
40. 40.What is the 29th term of the AP 2, 10, 18, 26, …? (a) 234 (b) 224 (c) 226 (d) 232

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