Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 659 · 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 14th term of the AP 10, 12, 14, 16, …? (a) 36 (b) 28 (c) 38 (d) 26
2. 2.What is the sum of all the whole numbers from 1 to 100? (a) 5050 (b) 5000 (c) 4950 (d) 10100
3. 3.Which term of the AP 3, 11, 19, 27, … is 243? (a) 31st (b) 33rd (c) 30th (d) 32nd
4. 4.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 435 (c) 465 (d) 450
5. 5.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 85 (b) 15 (c) 168 (d) 84
6. 6.What is the 22nd term of the AP 5, 8, 11, 14, …? (a) 63 (b) 68 (c) 71 (d) 66
7. 7.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 23 (b) 25 (c) 24 (d) 28
8. 8.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 462 (d) 441
9. 9.What is the 34th term of the AP 15, 23, 31, 39, …? (a) 264 (b) 279 (c) 272 (d) 287
10. 10.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 576 (d) 47
11. 11.Which term of the AP 4, 13, 22, 31, … is 283? (a) 33rd (b) 31st (c) 34th (d) 32nd
12. 12.What is the missing term in the AP 14, ?, 18, 20, 22? (a) 16 (b) 18 (c) 17 (d) 15
13. 13.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 153 (c) 342 (d) 171
14. 14.What is the 31st term of the AP 8, 11, 14, 17, …? (a) 93 (b) 90 (c) 101 (d) 98
15. 15.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 676 (d) 702
16. 16.Which term of the AP 3, 8, 13, 18, … is 48? (a) 11th (b) 9th (c) 12th (d) 10th
17. 17.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 610 (b) 53 (c) 330 (d) 305
18. 18.What is the missing term in the AP 7, 12, ?, 22, 27? (a) 17 (b) 16 (c) 18 (d) 22
19. 19.Which term of the AP 11, 15, 19, 23, … is 59? (a) 15th (b) 12th (c) 13th (d) 14th
20. 20.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 650 (d) 625
21. 21.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 812 (d) 784
22. 22.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 272 (d) 256
23. 23.Which term of the AP 16, 19, 22, 25, … is 55? (a) 15th (b) 14th (c) 13th (d) 16th
24. 24.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 14 (b) 100 (c) 55 (d) 50
25. 25.What is the 25th term of the AP 20, 28, 36, 44, …? (a) 212 (b) 220 (c) 200 (d) 192
26. 26.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 289 (c) 33 (d) 306
27. 27.What is the sum of the first 8 terms of the AP 6, 8, 10, …? (a) 112 (b) 208 (c) 104 (d) 20
28. 28.What is the 11th term of the AP 5, 7, 9, 11, …? (a) 22 (b) 25 (c) 20 (d) 27
29. 29.What is the 13th term of the AP 16, 18, 20, 22, …? (a) 40 (b) 24 (c) 42 (d) 26
30. 30.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3487 (c) 3486 (d) 3403
31. 31.What is the sum of all the whole numbers from 1 to 27? (a) 378 (b) 379 (c) 756 (d) 351
32. 32.What is the sum of all the whole numbers from 1 to 50? (a) 1275 (b) 1225 (c) 2550 (d) 1250
33. 33.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 132 (b) 32 (c) 117 (d) 234
34. 34.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 144 (d) 156
35. 35.Which term of the AP 12, 16, 20, 24, … is 156? (a) 38th (b) 39th (c) 37th (d) 36th
36. 36.What is the 21st term of the AP 19, 22, 25, 28, …? (a) 63 (b) 79 (c) 82 (d) 60
37. 37.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 368 (b) 44 (c) 208 (d) 184
38. 38.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 39 (d) 400
39. 39.What is the sum of all the whole numbers from 1 to 12? (a) 156 (b) 78 (c) 66 (d) 72
40. 40.What is the 11th term of the AP 11, 20, 29, 38, …? (a) 99 (b) 101 (c) 110 (d) 90

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