Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 994 · 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 16th term of the AP 1, 4, 7, 10, …? (a) 49 (b) 45 (c) 46 (d) 48
2. 2.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 840 (b) 68 (c) 456 (d) 420
3. 3.What is the 21st term of the AP 19, 21, 23, 25, …? (a) 61 (b) 59 (c) 42 (d) 40
4. 4.Which term of the AP 13, 15, 17, 19, … is 59? (a) 23rd (b) 26th (c) 25th (d) 24th
5. 5.What is the sum of all the whole numbers from 1 to 73? (a) 2702 (b) 2701 (c) 5402 (d) 2628
6. 6.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 66 (d) 121
7. 7.Which term of the AP 8, 17, 26, 35, … is 143? (a) 16th (b) 17th (c) 18th (d) 15th
8. 8.Which term of the AP 17, 25, 33, 41, … is 97? (a) 10th (b) 12th (c) 13th (d) 11th
9. 9.Which term of the AP 9, 18, 27, 36, … is 324? (a) 36th (b) 35th (c) 37th (d) 38th
10. 10.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 48 (b) 624 (c) 312 (d) 336
11. 11.What is the 29th term of the AP 5, 12, 19, 26, …? (a) 196 (b) 203 (c) 201 (d) 208
12. 12.What is the 39th term of the AP 17, 21, 25, 29, …? (a) 169 (b) 152 (c) 156 (d) 173
13. 13.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 36 (d) 11
14. 14.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 450 (b) 225 (c) 243 (d) 41
15. 15.What is the 37th term of the AP 20, 24, 28, 32, …? (a) 148 (b) 168 (c) 164 (d) 144
16. 16.What is the 31st term of the AP 20, 25, 30, 35, …? (a) 150 (b) 170 (c) 175 (d) 155
17. 17.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 40 (b) 564 (c) 300 (d) 282
18. 18.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 17 (b) 11 (c) 12 (d) 13
19. 19.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 289 (c) 153 (d) 306
20. 20.What is the 36th term of the AP 10, 18, 26, 34, …? (a) 290 (b) 288 (c) 280 (d) 298
21. 21.What is the 11th term of the AP 7, 16, 25, 34, …? (a) 90 (b) 99 (c) 97 (d) 106
22. 22.What is the missing term in the AP 14, 18, ?, 26, 30? (a) 21 (b) 22 (c) 26 (d) 23
23. 23.What is the missing term in the AP 16, 23, 30, ?, 44? (a) 38 (b) 36 (c) 37 (d) 44
24. 24.What is the missing term in the AP 17, ?, 25, 29, 33? (a) 25 (b) 22 (c) 20 (d) 21
25. 25.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 968 (c) 990 (d) 1980
26. 26.Which term of the AP 16, 24, 32, 40, … is 112? (a) 12th (b) 14th (c) 13th (d) 15th
27. 27.What is the 18th term of the AP 1, 10, 19, 28, …? (a) 153 (b) 154 (c) 163 (d) 162
28. 28.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 1190 (c) 578 (d) 595
29. 29.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 676 (c) 51 (d) 351
30. 30.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 841 (c) 57 (d) 870
31. 31.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 253 (c) 484 (d) 43
32. 32.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3872 (c) 3828 (d) 3916
33. 33.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1326 (c) 1275 (d) 1327
34. 34.What is the missing term in the AP 4, ?, 16, 22, 28? (a) 16 (b) 11 (c) 9 (d) 10
35. 35.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 255 (b) 510 (c) 48 (d) 280
36. 36.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 144 (b) 73 (c) 72 (d) 12
37. 37.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 25 (d) 15
38. 38.What is the missing term in the AP 4, 11, ?, 25, 32? (a) 17 (b) 25 (c) 18 (d) 19
39. 39.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 45 (c) 50 (d) 110
40. 40.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 230 (b) 420 (c) 39 (d) 210

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