Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 978 · 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 6 terms of the AP 9, 12, 15, …? (a) 198 (b) 99 (c) 24 (d) 108
2. 2.Which term of the AP 13, 19, 25, 31, … is 151? (a) 24th (b) 26th (c) 25th (d) 23rd
3. 3.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 40 (c) 70 (d) 35
4. 4.What is the 38th term of the AP 16, 23, 30, 37, …? (a) 259 (b) 266 (c) 282 (d) 275
5. 5.Which term of the AP 11, 15, 19, 23, … is 71? (a) 17th (b) 18th (c) 16th (d) 15th
6. 6.What is the 30th term of the AP 18, 23, 28, 33, …? (a) 163 (b) 150 (c) 168 (d) 145
7. 7.Which term of the AP 1, 6, 11, 16, … is 196? (a) 42nd (b) 40th (c) 41st (d) 39th
8. 8.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 465 (c) 435 (d) 930
9. 9.What is the missing term in the AP 1, ?, 9, 13, 17? (a) 5 (b) 4 (c) 6 (d) 9
10. 10.What is the 14th term of the AP 18, 24, 30, 36, …? (a) 84 (b) 78 (c) 102 (d) 96
11. 11.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 294 (b) 161 (c) 147 (d) 33
12. 12.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 380 (c) 190 (d) 37
13. 13.What is the sum of the first 9 terms of the AP 7, 10, 13, …? (a) 342 (b) 174 (c) 171 (d) 31
14. 14.What is the sum of all the whole numbers from 1 to 79? (a) 3160 (b) 3161 (c) 6320 (d) 3081
15. 15.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 406 (d) 812
16. 16.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 702 (c) 351 (d) 51
17. 17.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 420 (b) 39 (c) 230 (d) 210
18. 18.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 84 (b) 42 (c) 48 (d) 12
19. 19.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 360 (b) 180 (c) 198 (d) 36
20. 20.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 379 (c) 756 (d) 378
21. 21.Which term of the AP 4, 11, 18, 25, … is 116? (a) 19th (b) 18th (c) 16th (d) 17th
22. 22.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 161 (b) 322 (c) 38 (d) 166
23. 23.What is the 40th term of the AP 8, 15, 22, 29, …? (a) 273 (b) 280 (c) 281 (d) 288
24. 24.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 210 (c) 420 (d) 400
25. 25.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 630 (c) 595 (d) 1260
26. 26.What is the 34th term of the AP 10, 18, 26, 34, …? (a) 282 (b) 272 (c) 274 (d) 264
27. 27.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 2851 (c) 2850 (d) 5700
28. 28.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 441 (d) 41
29. 29.Which term of the AP 4, 10, 16, 22, … is 70? (a) 12th (b) 13th (c) 11th (d) 14th
30. 30.What is the 30th term of the AP 3, 7, 11, 15, …? (a) 119 (b) 116 (c) 123 (d) 120
31. 31.What is the 27th term of the AP 1, 4, 7, 10, …? (a) 81 (b) 82 (c) 79 (d) 78
32. 32.What is the 36th term of the AP 7, 16, 25, 34, …? (a) 331 (b) 322 (c) 324 (d) 315
33. 33.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 729 (c) 756 (d) 378
34. 34.What is the 15th term of the AP 10, 19, 28, 37, …? (a) 135 (b) 145 (c) 126 (d) 136
35. 35.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 57 (c) 870 (d) 435
36. 36.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 650 (c) 625 (d) 49
37. 37.What is the missing term in the AP 17, 26, 35, ?, 53? (a) 44 (b) 45 (c) 43 (d) 53
38. 38.What is the 21st term of the AP 3, 5, 7, 9, …? (a) 40 (b) 43 (c) 45 (d) 42
39. 39.What is the 40th term of the AP 17, 25, 33, 41, …? (a) 337 (b) 312 (c) 320 (d) 329
40. 40.What is the 14th term of the AP 19, 21, 23, 25, …? (a) 45 (b) 28 (c) 47 (d) 26

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