Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 124 · 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 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 625 (c) 325 (d) 650
2. 2.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 216 (b) 408 (c) 204 (d) 28
3. 3.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 289 (d) 306
4. 4.What is the missing term in the AP 12, 16, 20, ?, 28? (a) 23 (b) 24 (c) 25 (d) 28
5. 5.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 506 (c) 43 (d) 484
6. 6.Which term of the AP 20, 27, 34, 41, … is 181? (a) 25th (b) 23rd (c) 26th (d) 24th
7. 7.What is the 37th term of the AP 19, 22, 25, 28, …? (a) 108 (b) 130 (c) 111 (d) 127
8. 8.What is the sum of the first 9 terms of the AP 2, 8, 14, …? (a) 261 (b) 468 (c) 50 (d) 234
9. 9.What is the sum of all the whole numbers from 1 to 41? (a) 862 (b) 861 (c) 1722 (d) 820
10. 10.What is the sum of all the whole numbers from 1 to 40? (a) 1640 (b) 780 (c) 820 (d) 800
11. 11.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 17 (d) 90
12. 12.What is the 19th term of the AP 18, 21, 24, 27, …? (a) 75 (b) 54 (c) 57 (d) 72
13. 13.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 56 (b) 580 (c) 320 (d) 290
14. 14.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 40 (b) 43 (c) 14 (d) 80
15. 15.What is the 24th term of the AP 17, 25, 33, 41, …? (a) 184 (b) 201 (c) 209 (d) 192
16. 16.Which term of the AP 4, 7, 10, 13, … is 61? (a) 19th (b) 21st (c) 22nd (d) 20th
17. 17.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 631 (c) 595 (d) 630
18. 18.Which term of the AP 18, 27, 36, 45, … is 153? (a) 18th (b) 15th (c) 17th (d) 16th
19. 19.Which term of the AP 7, 9, 11, 13, … is 59? (a) 29th (b) 28th (c) 27th (d) 26th
20. 20.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 99 (b) 100 (c) 15 (d) 198
21. 21.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 57 (b) 12 (c) 114 (d) 60
22. 22.Which term of the AP 15, 19, 23, 27, … is 163? (a) 40th (b) 39th (c) 37th (d) 38th
23. 23.Which term of the AP 7, 12, 17, 22, … is 112? (a) 22nd (b) 24th (c) 21st (d) 23rd
24. 24.What is the 36th term of the AP 19, 27, 35, 43, …? (a) 307 (b) 280 (c) 288 (d) 299
25. 25.Which term of the AP 5, 13, 21, 29, … is 93? (a) 11th (b) 12th (c) 13th (d) 14th
26. 26.What is the 30th term of the AP 2, 11, 20, 29, …? (a) 270 (b) 272 (c) 263 (d) 261
27. 27.What is the 21st term of the AP 7, 16, 25, 34, …? (a) 196 (b) 187 (c) 180 (d) 189
28. 28.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 180 (b) 30 (c) 105 (d) 90
29. 29.What is the missing term in the AP 4, ?, 12, 16, 20? (a) 9 (b) 12 (c) 7 (d) 8
30. 30.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 10 (b) 7 (c) 8 (d) 9
31. 31.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 27 (b) 35 (c) 26 (d) 28
32. 32.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 351 (c) 51 (d) 676
33. 33.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 28 (d) 13
34. 34.Which term of the AP 16, 23, 30, 37, … is 93? (a) 12th (b) 14th (c) 13th (d) 11th
35. 35.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 176 (b) 34 (c) 160 (d) 320
36. 36.What is the 35th term of the AP 15, 20, 25, 30, …? (a) 175 (b) 190 (c) 185 (d) 170
37. 37.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 275 (b) 550 (c) 40 (d) 278
38. 38.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 196 (b) 43 (c) 175 (d) 350
39. 39.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 24 (b) 144 (c) 288 (d) 153
40. 40.What is the 35th term of the AP 13, 17, 21, 25, …? (a) 149 (b) 153 (c) 136 (d) 140

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