Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 527 · 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 10th term of the AP 18, 25, 32, 39, …? (a) 81 (b) 70 (c) 88 (d) 63
2. 2.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 228 (b) 29 (c) 432 (d) 216
3. 3.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 126 (b) 63 (c) 15 (d) 70
4. 4.What is the 13th term of the AP 10, 16, 22, 28, …? (a) 72 (b) 82 (c) 88 (d) 78
5. 5.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 98 (b) 49 (c) 13 (d) 56
6. 6.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 2145 (c) 4422 (d) 2211
7. 7.What is the missing term in the AP 20, 22, ?, 26, 28? (a) 26 (b) 25 (c) 24 (d) 23
8. 8.Which term of the AP 4, 12, 20, 28, … is 284? (a) 38th (b) 35th (c) 37th (d) 36th
9. 9.What is the missing term in the AP 3, 7, 11, ?, 19? (a) 14 (b) 16 (c) 15 (d) 19
10. 10.What is the missing term in the AP 1, ?, 11, 16, 21? (a) 6 (b) 11 (c) 5 (d) 7
11. 11.Which term of the AP 9, 12, 15, 18, … is 93? (a) 31st (b) 29th (c) 28th (d) 30th
12. 12.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 19 (b) 22 (c) 18 (d) 17
13. 13.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 209 (b) 198 (c) 396 (d) 28
14. 14.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 6162 (c) 3042 (d) 3003
15. 15.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 18 (b) 156 (c) 300 (d) 150
16. 16.What is the 17th term of the AP 2, 7, 12, 17, …? (a) 85 (b) 87 (c) 82 (d) 80
17. 17.What is the missing term in the AP 4, 11, ?, 25, 32? (a) 25 (b) 18 (c) 17 (d) 19
18. 18.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 15 (b) 75 (c) 78 (d) 150
19. 19.What is the 19th term of the AP 15, 19, 23, 27, …? (a) 72 (b) 76 (c) 87 (d) 91
20. 20.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 110 (b) 120 (c) 20 (d) 220
21. 21.What is the 27th term of the AP 9, 17, 25, 33, …? (a) 225 (b) 216 (c) 208 (d) 217
22. 22.Which term of the AP 9, 11, 13, 15, … is 43? (a) 20th (b) 17th (c) 18th (d) 19th
23. 23.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 625 (c) 650 (d) 325
24. 24.Which term of the AP 6, 14, 22, 30, … is 214? (a) 27th (b) 26th (c) 29th (d) 28th
25. 25.What is the 40th term of the AP 19, 23, 27, 31, …? (a) 156 (b) 179 (c) 175 (d) 160
26. 26.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 63 (b) 126 (c) 64 (d) 11
27. 27.What is the 25th term of the AP 11, 18, 25, 32, …? (a) 186 (b) 179 (c) 175 (d) 168
28. 28.Which term of the AP 1, 6, 11, 16, … is 196? (a) 39th (b) 41st (c) 40th (d) 42nd
29. 29.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3655 (c) 3570 (d) 3656
30. 30.What is the 29th term of the AP 19, 21, 23, 25, …? (a) 58 (b) 56 (c) 75 (d) 77
31. 31.What is the missing term in the AP 11, ?, 15, 17, 19? (a) 15 (b) 13 (c) 14 (d) 12
32. 32.What is the 25th term of the AP 7, 15, 23, 31, …? (a) 200 (b) 192 (c) 207 (d) 199
33. 33.Which term of the AP 2, 7, 12, 17, … is 42? (a) 8th (b) 9th (c) 11th (d) 10th
34. 34.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 380 (d) 361
35. 35.Which term of the AP 7, 12, 17, 22, … is 107? (a) 21st (b) 23rd (c) 20th (d) 22nd
36. 36.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1352 (c) 1326 (d) 1378
37. 37.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 6 (b) 4 (c) 7 (d) 5
38. 38.What is the 34th term of the AP 4, 7, 10, 13, …? (a) 102 (b) 103 (c) 106 (d) 99
39. 39.What is the sum of all the whole numbers from 1 to 46? (a) 2162 (b) 1035 (c) 1081 (d) 1058
40. 40.What is the 22nd term of the AP 19, 22, 25, 28, …? (a) 63 (b) 82 (c) 85 (d) 66

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