Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 379 · 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 19th term of the AP 7, 11, 15, 19, …? (a) 83 (b) 79 (c) 76 (d) 72
2. 2.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 120 (b) 63 (c) 60 (d) 18
3. 3.What is the 31st term of the AP 3, 12, 21, 30, …? (a) 282 (b) 279 (c) 273 (d) 270
4. 4.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 465 (c) 900 (d) 59
5. 5.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 67 (c) 132 (d) 55
6. 6.What is the missing term in the AP 14, 20, 26, ?, 38? (a) 32 (b) 31 (c) 38 (d) 33
7. 7.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 31 (b) 190 (c) 175 (d) 350
8. 8.What is the 22nd term of the AP 4, 8, 12, 16, …? (a) 84 (b) 92 (c) 89 (d) 88
9. 9.What is the 15th term of the AP 5, 8, 11, 14, …? (a) 45 (b) 50 (c) 42 (d) 47
10. 10.What is the 13th term of the AP 6, 8, 10, 12, …? (a) 24 (b) 30 (c) 32 (d) 26
11. 11.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 110 (b) 125 (c) 220 (d) 34
12. 12.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 18 (b) 252 (c) 127 (d) 126
13. 13.What is the missing term in the AP 8, 12, ?, 20, 24? (a) 16 (b) 15 (c) 20 (d) 17
14. 14.What is the 20th term of the AP 16, 18, 20, 22, …? (a) 56 (b) 40 (c) 54 (d) 38
15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 400 (d) 39
16. 16.Which term of the AP 18, 25, 32, 39, … is 263? (a) 37th (b) 35th (c) 38th (d) 36th
17. 17.What is the 14th term of the AP 3, 5, 7, 9, …? (a) 29 (b) 31 (c) 26 (d) 28
18. 18.Which term of the AP 6, 14, 22, 30, … is 70? (a) 8th (b) 11th (c) 9th (d) 10th
19. 19.What is the 10th term of the AP 4, 10, 16, 22, …? (a) 64 (b) 58 (c) 60 (d) 54
20. 20.What is the 33rd term of the AP 13, 15, 17, 19, …? (a) 79 (b) 77 (c) 64 (d) 66
21. 21.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 45 (b) 225 (c) 230 (d) 450
22. 22.What is the 36th term of the AP 7, 15, 23, 31, …? (a) 287 (b) 280 (c) 295 (d) 288
23. 23.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 19 (b) 22 (c) 18 (d) 17
24. 24.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 37 (b) 46 (c) 38 (d) 36
25. 25.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 46 (b) 260 (c) 470 (d) 235
26. 26.What is the 23rd term of the AP 1, 5, 9, 13, …? (a) 88 (b) 92 (c) 89 (d) 93
27. 27.What is the 10th term of the AP 18, 21, 24, 27, …? (a) 30 (b) 27 (c) 45 (d) 48
28. 28.What is the 28th term of the AP 19, 28, 37, 46, …? (a) 252 (b) 271 (c) 243 (d) 262
29. 29.What is the missing term in the AP 19, ?, 23, 25, 27? (a) 20 (b) 23 (c) 21 (d) 22
30. 30.What is the 11th term of the AP 8, 10, 12, 14, …? (a) 30 (b) 20 (c) 28 (d) 22
31. 31.Which term of the AP 18, 20, 22, 24, … is 68? (a) 25th (b) 27th (c) 34th (d) 26th
32. 32.What is the 19th term of the AP 1, 4, 7, 10, …? (a) 58 (b) 57 (c) 55 (d) 54
33. 33.What is the 33rd term of the AP 14, 22, 30, 38, …? (a) 264 (b) 278 (c) 256 (d) 270
34. 34.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 702 (c) 351 (d) 676
35. 35.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 43 (c) 253 (d) 506
36. 36.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 45 (c) 552 (d) 276
37. 37.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 576 (d) 47
38. 38.What is the missing term in the AP 8, 11, ?, 17, 20? (a) 15 (b) 14 (c) 17 (d) 13
39. 39.What is the missing term in the AP 4, ?, 22, 31, 40? (a) 13 (b) 12 (c) 14 (d) 22
40. 40.Which term of the AP 11, 18, 25, 32, … is 95? (a) 15th (b) 14th (c) 12th (d) 13th

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