Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 734 · 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 9 terms of the AP 9, 12, 15, …? (a) 33 (b) 378 (c) 192 (d) 189
2. 2.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 144 (d) 156
3. 3.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 552 (d) 529
4. 4.What is the sum of all the whole numbers from 1 to 38? (a) 1482 (b) 722 (c) 703 (d) 741
5. 5.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 75 (b) 24 (c) 140 (d) 70
6. 6.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 2080 (c) 4160 (d) 2048
7. 7.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 11 (b) 15 (c) 12 (d) 13
8. 8.What is the 28th term of the AP 6, 14, 22, 30, …? (a) 230 (b) 222 (c) 216 (d) 224
9. 9.What is the 24th term of the AP 14, 23, 32, 41, …? (a) 230 (b) 207 (c) 216 (d) 221
10. 10.What is the 40th term of the AP 20, 22, 24, 26, …? (a) 78 (b) 98 (c) 80 (d) 100
11. 11.What is the 14th term of the AP 5, 10, 15, 20, …? (a) 71 (b) 65 (c) 75 (d) 70
12. 12.Which term of the AP 1, 7, 13, 19, … is 229? (a) 39th (b) 41st (c) 38th (d) 40th
13. 13.Which term of the AP 15, 18, 21, 24, … is 129? (a) 43rd (b) 38th (c) 40th (d) 39th
14. 14.What is the 18th term of the AP 13, 15, 17, 19, …? (a) 34 (b) 36 (c) 49 (d) 47
15. 15.What is the sum of all the whole numbers from 1 to 53? (a) 1431 (b) 1378 (c) 2862 (d) 1432
16. 16.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 170 (b) 29 (c) 100 (d) 85
17. 17.Which term of the AP 14, 16, 18, 20, … is 88? (a) 39th (b) 37th (c) 38th (d) 44th
18. 18.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 35 (d) 324
19. 19.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 484 (c) 43 (d) 506
20. 20.What is the 39th term of the AP 13, 19, 25, 31, …? (a) 247 (b) 228 (c) 234 (d) 241
21. 21.Which term of the AP 1, 8, 15, 22, … is 113? (a) 19th (b) 16th (c) 17th (d) 18th
22. 22.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 25 (b) 23 (c) 24 (d) 28
23. 23.What is the sum of the first 10 terms of the AP 7, 10, 13, …? (a) 220 (b) 205 (c) 410 (d) 34
24. 24.What is the sum of all the whole numbers from 1 to 85? (a) 3655 (b) 7310 (c) 3656 (d) 3570
25. 25.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 4 (b) 7 (c) 5 (d) 3
26. 26.Which term of the AP 4, 8, 12, 16, … is 144? (a) 36th (b) 35th (c) 38th (d) 37th
27. 27.What is the 34th term of the AP 2, 6, 10, 14, …? (a) 138 (b) 136 (c) 132 (d) 134
28. 28.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 84 (b) 15 (c) 85 (d) 168
29. 29.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 45 (b) 11 (c) 46 (d) 90
30. 30.Which term of the AP 2, 7, 12, 17, … is 82? (a) 16th (b) 19th (c) 17th (d) 18th
31. 31.What is the 33rd term of the AP 11, 17, 23, 29, …? (a) 192 (b) 198 (c) 203 (d) 209
32. 32.What is the 39th term of the AP 14, 21, 28, 35, …? (a) 273 (b) 287 (c) 266 (d) 280
33. 33.What is the missing term in the AP 17, 25, ?, 41, 49? (a) 32 (b) 34 (c) 41 (d) 33
34. 34.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 66 (b) 63 (c) 13 (d) 126
35. 35.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 59 (c) 900 (d) 465
36. 36.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 11 (b) 120 (c) 64 (d) 60
37. 37.Which term of the AP 11, 17, 23, 29, … is 101? (a) 17th (b) 18th (c) 15th (d) 16th
38. 38.What is the 29th term of the AP 12, 14, 16, 18, …? (a) 70 (b) 68 (c) 58 (d) 56
39. 39.What is the 16th term of the AP 3, 12, 21, 30, …? (a) 135 (b) 144 (c) 147 (d) 138
40. 40.Which term of the AP 2, 8, 14, 20, … is 80? (a) 16th (b) 14th (c) 13th (d) 15th

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