Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 912 · 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 10 terms of the AP 6, 9, 12, …? (a) 210 (b) 195 (c) 33 (d) 390
2. 2.What is the 28th term of the AP 19, 28, 37, 46, …? (a) 243 (b) 262 (c) 252 (d) 271
3. 3.What is the 18th term of the AP 6, 10, 14, 18, …? (a) 72 (b) 74 (c) 68 (d) 78
4. 4.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 190 (c) 191 (d) 380
5. 5.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 220 (b) 110 (c) 120 (d) 20
6. 6.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 552 (d) 529
7. 7.What is the missing term in the AP 8, 16, ?, 32, 40? (a) 25 (b) 32 (c) 23 (d) 24
8. 8.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 45 (d) 17
9. 9.What is the missing term in the AP 3, 12, 21, ?, 39? (a) 31 (b) 39 (c) 30 (d) 29
10. 10.Which term of the AP 19, 22, 25, 28, … is 67? (a) 19th (b) 18th (c) 17th (d) 16th
11. 11.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 80 (b) 70 (c) 22 (d) 140
12. 12.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 676 (d) 702
13. 13.What is the 39th term of the AP 8, 17, 26, 35, …? (a) 350 (b) 359 (c) 342 (d) 351
14. 14.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3321 (c) 3240 (d) 3322
15. 15.What is the sum of all the whole numbers from 1 to 61? (a) 1892 (b) 3782 (c) 1830 (d) 1891
16. 16.What is the missing term in the AP 6, 8, ?, 12, 14? (a) 11 (b) 9 (c) 10 (d) 12
17. 17.What is the 14th term of the AP 3, 12, 21, 30, …? (a) 129 (b) 126 (c) 120 (d) 117
18. 18.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 506 (b) 256 (c) 38 (d) 253
19. 19.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 20 (b) 330 (c) 166 (d) 165
20. 20.What is the 40th term of the AP 2, 7, 12, 17, …? (a) 197 (b) 200 (c) 202 (d) 195
21. 21.What is the sum of all the whole numbers from 1 to 100? (a) 10100 (b) 5050 (c) 5000 (d) 4950
22. 22.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 210 (c) 400 (d) 420
23. 23.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 65 (b) 23 (c) 130 (d) 70
24. 24.What is the missing term in the AP 7, 10, ?, 16, 19? (a) 14 (b) 12 (c) 13 (d) 16
25. 25.Which term of the AP 20, 26, 32, 38, … is 140? (a) 23rd (b) 22nd (c) 20th (d) 21st
26. 26.What is the 21st term of the AP 17, 22, 27, 32, …? (a) 105 (b) 117 (c) 122 (d) 100
27. 27.Which term of the AP 17, 23, 29, 35, … is 125? (a) 21st (b) 19th (c) 18th (d) 20th
28. 28.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 702 (c) 351 (d) 325
29. 29.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 31 (b) 240 (c) 480 (d) 252
30. 30.What is the sum of the first 8 terms of the AP 4, 7, 10, …? (a) 128 (b) 232 (c) 25 (d) 116
31. 31.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 3306 (c) 1596 (d) 1654
32. 32.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 196 (c) 27 (d) 105
33. 33.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 272 (c) 136 (d) 256
34. 34.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 497 (c) 465 (d) 496
35. 35.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 34 (b) 396 (c) 198 (d) 201
36. 36.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 100 (b) 12 (c) 51 (d) 50
37. 37.Which term of the AP 20, 23, 26, 29, … is 137? (a) 41st (b) 40th (c) 42nd (d) 39th
38. 38.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 465 (c) 930 (d) 59
39. 39.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 561 (c) 1122 (d) 528
40. 40.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 67 (c) 55 (d) 66

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