Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 441 · 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 sum of the first 10 terms of the AP 7, 12, 17, …? (a) 590 (b) 295 (c) 320 (d) 52
2. 2.What is the 25th term of the AP 18, 27, 36, 45, …? (a) 225 (b) 234 (c) 243 (d) 216
3. 3.Which term of the AP 2, 10, 18, 26, … is 258? (a) 34th (b) 35th (c) 33rd (d) 32nd
4. 4.What is the 20th term of the AP 5, 14, 23, 32, …? (a) 185 (b) 171 (c) 180 (d) 176
5. 5.Which term of the AP 11, 19, 27, 35, … is 67? (a) 9th (b) 10th (c) 7th (d) 8th
6. 6.What is the 13th term of the AP 19, 28, 37, 46, …? (a) 136 (b) 117 (c) 127 (d) 108
7. 7.What is the missing term in the AP 16, ?, 26, 31, 36? (a) 26 (b) 22 (c) 20 (d) 21
8. 8.Which term of the AP 4, 10, 16, 22, … is 166? (a) 28th (b) 27th (c) 29th (d) 30th
9. 9.Which term of the AP 12, 15, 18, 21, … is 39? (a) 10th (b) 13th (c) 9th (d) 11th
10. 10.What is the missing term in the AP 17, 20, 23, ?, 29? (a) 26 (b) 27 (c) 25 (d) 29
11. 11.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 140 (b) 70 (c) 18 (d) 75
12. 12.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 187 (b) 374 (c) 32 (d) 190
13. 13.What is the 11th term of the AP 17, 22, 27, 32, …? (a) 67 (b) 55 (c) 50 (d) 72
14. 14.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 240 (b) 456 (c) 30 (d) 228
15. 15.What is the 30th term of the AP 20, 26, 32, 38, …? (a) 174 (b) 180 (c) 200 (d) 194
16. 16.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 29 (b) 170 (c) 100 (d) 85
17. 17.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 47 (d) 576
18. 18.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 497 (c) 496 (d) 992
19. 19.Which term of the AP 12, 15, 18, 21, … is 63? (a) 17th (b) 21st (c) 18th (d) 19th
20. 20.What is the 10th term of the AP 8, 12, 16, 20, …? (a) 48 (b) 44 (c) 36 (d) 40
21. 21.Which term of the AP 11, 16, 21, 26, … is 56? (a) 9th (b) 12th (c) 11th (d) 10th
22. 22.What is the missing term in the AP 4, ?, 14, 19, 24? (a) 14 (b) 8 (c) 10 (d) 9
23. 23.What is the 28th term of the AP 2, 6, 10, 14, …? (a) 112 (b) 114 (c) 110 (d) 108
24. 24.What is the 36th term of the AP 4, 7, 10, 13, …? (a) 108 (b) 112 (c) 109 (d) 105
25. 25.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 18 (b) 21 (c) 19 (d) 20
26. 26.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 49 (d) 56
27. 27.Which term of the AP 7, 13, 19, 25, … is 145? (a) 23rd (b) 26th (c) 24th (d) 25th
28. 28.What is the 15th term of the AP 15, 20, 25, 30, …? (a) 90 (b) 75 (c) 85 (d) 70
29. 29.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 39 (c) 400 (d) 210
30. 30.Which term of the AP 17, 25, 33, 41, … is 161? (a) 21st (b) 19th (c) 20th (d) 18th
31. 31.Which term of the AP 19, 23, 27, 31, … is 175? (a) 41st (b) 40th (c) 39th (d) 42nd
32. 32.What is the missing term in the AP 5, ?, 23, 32, 41? (a) 13 (b) 15 (c) 23 (d) 14
33. 33.What is the sum of all the whole numbers from 1 to 94? (a) 4371 (b) 8930 (c) 4418 (d) 4465
34. 34.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 625 (c) 650 (d) 49
35. 35.What is the sum of all the whole numbers from 1 to 62? (a) 3906 (b) 1891 (c) 1922 (d) 1953
36. 36.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3655 (c) 3741 (d) 3698
37. 37.What is the missing term in the AP 11, ?, 21, 26, 31? (a) 21 (b) 16 (c) 15 (d) 17
38. 38.What is the 30th term of the AP 8, 13, 18, 23, …? (a) 145 (b) 153 (c) 150 (d) 158
39. 39.Which term of the AP 17, 26, 35, 44, … is 170? (a) 18th (b) 19th (c) 20th (d) 17th
40. 40.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 123 (b) 246 (c) 33 (d) 138

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