Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 917 · 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 all the whole numbers from 1 to 37? (a) 666 (b) 1406 (c) 704 (d) 703
2. 2.What is the 18th term of the AP 3, 10, 17, 24, …? (a) 119 (b) 129 (c) 126 (d) 122
3. 3.What is the sum of all the whole numbers from 1 to 97? (a) 4753 (b) 9506 (c) 4656 (d) 4754
4. 4.What is the 13th term of the AP 14, 21, 28, 35, …? (a) 84 (b) 91 (c) 105 (d) 98
5. 5.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 30 (c) 9 (d) 15
6. 6.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 245 (b) 37 (c) 242 (d) 484
7. 7.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 192 (b) 26 (c) 180 (d) 360
8. 8.Which term of the AP 7, 13, 19, 25, … is 61? (a) 12th (b) 10th (c) 11th (d) 9th
9. 9.What is the sum of all the whole numbers from 1 to 77? (a) 3004 (b) 3003 (c) 2926 (d) 6006
10. 10.What is the sum of all the whole numbers from 1 to 95? (a) 4561 (b) 4560 (c) 9120 (d) 4465
11. 11.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 169 (d) 182
12. 12.What is the missing term in the AP 4, ?, 8, 10, 12? (a) 5 (b) 6 (c) 7 (d) 8
13. 13.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 58 (b) 306 (c) 612 (d) 333
14. 14.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 136 (b) 28 (c) 133 (d) 266
15. 15.What is the 30th term of the AP 2, 10, 18, 26, …? (a) 242 (b) 234 (c) 240 (d) 232
16. 16.Which term of the AP 8, 16, 24, 32, … is 64? (a) 9th (b) 7th (c) 10th (d) 8th
17. 17.Which term of the AP 18, 20, 22, 24, … is 60? (a) 23rd (b) 22nd (c) 30th (d) 21st
18. 18.What is the sum of all the whole numbers from 1 to 43? (a) 903 (b) 946 (c) 947 (d) 1892
19. 19.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 272 (d) 31
20. 20.What is the missing term in the AP 7, 16, ?, 34, 43? (a) 26 (b) 24 (c) 34 (d) 25
21. 21.What is the sum of all the whole numbers from 1 to 50? (a) 1275 (b) 1250 (c) 2550 (d) 1225
22. 22.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 140 (b) 70 (c) 13 (d) 71
23. 23.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 192 (b) 36 (c) 176 (d) 352
24. 24.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 20 (b) 77 (c) 80 (d) 154
25. 25.Which term of the AP 20, 22, 24, 26, … is 44? (a) 22nd (b) 13th (c) 14th (d) 12th
26. 26.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 552 (c) 45 (d) 529
27. 27.Which term of the AP 14, 16, 18, 20, … is 58? (a) 29th (b) 23rd (c) 24th (d) 22nd
28. 28.Which term of the AP 3, 9, 15, 21, … is 171? (a) 29th (b) 30th (c) 28th (d) 31st
29. 29.What is the 38th term of the AP 2, 4, 6, 8, …? (a) 78 (b) 77 (c) 74 (d) 76
30. 30.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 180 (b) 168 (c) 25 (d) 336
31. 31.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 30 (b) 312 (c) 168 (d) 156
32. 32.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2926 (c) 2850 (d) 2888
33. 33.Which term of the AP 4, 6, 8, 10, … is 30? (a) 16th (b) 15th (c) 13th (d) 14th
34. 34.Which term of the AP 15, 19, 23, 27, … is 143? (a) 35th (b) 34th (c) 33rd (d) 32nd
35. 35.What is the sum of all the whole numbers from 1 to 85? (a) 3656 (b) 3655 (c) 7310 (d) 3570
36. 36.What is the missing term in the AP 15, ?, 19, 21, 23? (a) 16 (b) 18 (c) 17 (d) 19
37. 37.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 1431 (c) 2862 (d) 1378
38. 38.What is the missing term in the AP 6, 15, 24, ?, 42? (a) 34 (b) 42 (c) 32 (d) 33
39. 39.What is the 24th term of the AP 19, 27, 35, 43, …? (a) 211 (b) 192 (c) 184 (d) 203
40. 40.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 210 (c) 400 (d) 420

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