Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 112 · 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.Which term of the AP 13, 18, 23, 28, … is 108? (a) 22nd (b) 21st (c) 19th (d) 20th
2. 2.Which term of the AP 2, 5, 8, 11, … is 110? (a) 38th (b) 37th (c) 36th (d) 39th
3. 3.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 60 (b) 21 (c) 110 (d) 55
4. 4.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 235 (b) 470 (c) 260 (d) 46
5. 5.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 56 (b) 28 (c) 29 (d) 7
6. 6.What is the missing term in the AP 6, ?, 20, 27, 34? (a) 20 (b) 14 (c) 13 (d) 12
7. 7.What is the 17th term of the AP 12, 14, 16, 18, …? (a) 46 (b) 32 (c) 34 (d) 44
8. 8.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 528 (c) 562 (d) 561
9. 9.What is the missing term in the AP 11, 20, 29, ?, 47? (a) 47 (b) 37 (c) 39 (d) 38
10. 10.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 630 (c) 648 (d) 666
11. 11.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 29 (b) 23 (c) 24 (d) 25
12. 12.What is the 11th term of the AP 19, 24, 29, 34, …? (a) 74 (b) 50 (c) 69 (d) 55
13. 13.What is the 11th term of the AP 12, 19, 26, 33, …? (a) 70 (b) 77 (c) 82 (d) 89
14. 14.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 176 (b) 320 (c) 34 (d) 160
15. 15.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4560 (c) 4561 (d) 4465
16. 16.Which term of the AP 5, 13, 21, 29, … is 101? (a) 13th (b) 12th (c) 14th (d) 15th
17. 17.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 160 (b) 88 (c) 17 (d) 80
18. 18.Which term of the AP 6, 11, 16, 21, … is 51? (a) 9th (b) 12th (c) 10th (d) 11th
19. 19.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 5852 (c) 2926 (d) 2850
20. 20.Which term of the AP 2, 5, 8, 11, … is 29? (a) 12th (b) 9th (c) 10th (d) 11th
21. 21.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 370 (b) 340 (c) 680 (d) 61
22. 22.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 18 (b) 50 (c) 100 (d) 60
23. 23.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 28 (d) 49
24. 24.What is the missing term in the AP 7, ?, 25, 34, 43? (a) 17 (b) 15 (c) 16 (d) 25
25. 25.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 56 (b) 341 (c) 346 (d) 682
26. 26.Which term of the AP 17, 21, 25, 29, … is 89? (a) 18th (b) 21st (c) 20th (d) 19th
27. 27.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 43 (c) 253 (d) 506
28. 28.What is the missing term in the AP 17, 24, 31, ?, 45? (a) 38 (b) 37 (c) 39 (d) 45
29. 29.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 12 (b) 14 (c) 16 (d) 13
30. 30.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 200 (b) 40 (c) 180 (d) 360
31. 31.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 990 (c) 1035 (d) 2070
32. 32.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 66 (d) 121
33. 33.What is the missing term in the AP 7, 9, ?, 13, 15? (a) 12 (b) 11 (c) 13 (d) 10
34. 34.What is the 33rd term of the AP 6, 8, 10, 12, …? (a) 72 (b) 64 (c) 66 (d) 70
35. 35.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3570 (c) 3655 (d) 3656
36. 36.What is the 27th term of the AP 13, 18, 23, 28, …? (a) 135 (b) 148 (c) 143 (d) 130
37. 37.What is the 37th term of the AP 14, 23, 32, 41, …? (a) 347 (b) 324 (c) 333 (d) 338
38. 38.What is the 32nd term of the AP 6, 8, 10, 12, …? (a) 70 (b) 64 (c) 62 (d) 68
39. 39.What is the 38th term of the AP 7, 9, 11, 13, …? (a) 83 (b) 81 (c) 74 (d) 76
40. 40.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 702 (c) 51 (d) 351

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