Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 59 · 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 38th term of the AP 9, 14, 19, 24, …? (a) 185 (b) 194 (c) 199 (d) 190
2. 2.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 45 (b) 48 (c) 90 (d) 10
3. 3.Which term of the AP 20, 26, 32, 38, … is 74? (a) 9th (b) 11th (c) 12th (d) 10th
4. 4.Which term of the AP 17, 21, 25, 29, … is 73? (a) 15th (b) 16th (c) 14th (d) 17th
5. 5.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 156 (c) 23 (d) 78
6. 6.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 506 (b) 256 (c) 253 (d) 38
7. 7.Which term of the AP 10, 15, 20, 25, … is 165? (a) 33rd (b) 31st (c) 34th (d) 32nd
8. 8.What is the sum of all the whole numbers from 1 to 31? (a) 496 (b) 497 (c) 465 (d) 992
9. 9.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 22 (b) 19 (c) 18 (d) 17
10. 10.What is the 30th term of the AP 11, 17, 23, 29, …? (a) 191 (b) 174 (c) 180 (d) 185
11. 11.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 19 (b) 24 (c) 20 (d) 21
12. 12.What is the sum of all the whole numbers from 1 to 83? (a) 3486 (b) 3487 (c) 3403 (d) 6972
13. 13.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 60 (b) 35 (c) 30 (d) 10
14. 14.What is the missing term in the AP 20, ?, 38, 47, 56? (a) 38 (b) 28 (c) 30 (d) 29
15. 15.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 126 (b) 18 (c) 72 (d) 63
16. 16.What is the 22nd term of the AP 1, 3, 5, 7, …? (a) 45 (b) 44 (c) 43 (d) 42
17. 17.What is the 19th term of the AP 2, 11, 20, 29, …? (a) 173 (b) 171 (c) 164 (d) 162
18. 18.Which term of the AP 1, 3, 5, 7, … is 15? (a) 8th (b) 10th (c) 9th (d) 7th
19. 19.What is the 34th term of the AP 5, 10, 15, 20, …? (a) 170 (b) 165 (c) 171 (d) 175
20. 20.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 51 (c) 676 (d) 351
21. 21.What is the 35th term of the AP 19, 22, 25, 28, …? (a) 124 (b) 121 (c) 105 (d) 102
22. 22.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 600 (d) 300
23. 23.What is the 22nd term of the AP 14, 21, 28, 35, …? (a) 154 (b) 161 (c) 168 (d) 147
24. 24.What is the missing term in the AP 2, 8, ?, 20, 26? (a) 20 (b) 14 (c) 13 (d) 15
25. 25.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 378 (d) 729
26. 26.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 2211 (c) 4556 (d) 2279
27. 27.What is the missing term in the AP 12, ?, 30, 39, 48? (a) 30 (b) 22 (c) 21 (d) 20
28. 28.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 360 (b) 180 (c) 200 (d) 40
29. 29.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 126 (b) 70 (c) 15 (d) 63
30. 30.What is the 38th term of the AP 10, 18, 26, 34, …? (a) 314 (b) 296 (c) 304 (d) 306
31. 31.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 196 (c) 27 (d) 105
32. 32.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 190 (d) 37
33. 33.What is the missing term in the AP 4, ?, 20, 28, 36? (a) 12 (b) 13 (c) 20 (d) 11
34. 34.What is the 40th term of the AP 10, 19, 28, 37, …? (a) 370 (b) 360 (c) 351 (d) 361
35. 35.What is the 17th term of the AP 20, 22, 24, 26, …? (a) 54 (b) 52 (c) 32 (d) 34
36. 36.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 16 (b) 14 (c) 12 (d) 13
37. 37.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 930 (d) 900
38. 38.Which term of the AP 13, 18, 23, 28, … is 68? (a) 14th (b) 11th (c) 12th (d) 13th
39. 39.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 3828 (c) 3741 (d) 7656
40. 40.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 150 (b) 84 (c) 75 (d) 20

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