Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 762 · 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 6 terms of the AP 10, 15, 20, …? (a) 270 (b) 135 (c) 35 (d) 150
2. 2.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 174 (b) 22 (c) 87 (d) 96
3. 3.What is the sum of all the whole numbers from 1 to 37? (a) 1406 (b) 666 (c) 703 (d) 704
4. 4.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3486 (c) 3570 (d) 3528
5. 5.Which term of the AP 6, 9, 12, 15, … is 117? (a) 40th (b) 38th (c) 39th (d) 37th
6. 6.Which term of the AP 6, 13, 20, 27, … is 230? (a) 34th (b) 35th (c) 32nd (d) 33rd
7. 7.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 4371 (c) 8742 (d) 4372
8. 8.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 44 (b) 208 (c) 368 (d) 184
9. 9.What is the 36th term of the AP 4, 11, 18, 25, …? (a) 252 (b) 249 (c) 245 (d) 256
10. 10.What is the missing term in the AP 16, 25, 34, ?, 52? (a) 52 (b) 43 (c) 42 (d) 44
11. 11.What is the 13th term of the AP 15, 22, 29, 36, …? (a) 84 (b) 106 (c) 99 (d) 91
12. 12.What is the missing term in the AP 10, ?, 24, 31, 38? (a) 16 (b) 18 (c) 24 (d) 17
13. 13.What is the 28th term of the AP 13, 15, 17, 19, …? (a) 54 (b) 56 (c) 69 (d) 67
14. 14.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 30 (b) 128 (c) 256 (d) 144
15. 15.What is the 33rd term of the AP 3, 11, 19, 27, …? (a) 256 (b) 264 (c) 259 (d) 267
16. 16.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 328 (b) 38 (c) 164 (d) 184
17. 17.Which term of the AP 12, 19, 26, 33, … is 271? (a) 37th (b) 39th (c) 38th (d) 40th
18. 18.What is the missing term in the AP 4, 13, 22, ?, 40? (a) 30 (b) 32 (c) 40 (d) 31
19. 19.Which term of the AP 19, 21, 23, 25, … is 63? (a) 24th (b) 25th (c) 22nd (d) 23rd
20. 20.What is the missing term in the AP 1, 6, ?, 16, 21? (a) 12 (b) 10 (c) 11 (d) 16
21. 21.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 372 (b) 186 (c) 192 (d) 21
22. 22.What is the sum of all the whole numbers from 1 to 61? (a) 3782 (b) 1830 (c) 1892 (d) 1891
23. 23.What is the sum of all the whole numbers from 1 to 74? (a) 2775 (b) 5550 (c) 2701 (d) 2738
24. 24.Which term of the AP 3, 8, 13, 18, … is 58? (a) 14th (b) 11th (c) 12th (d) 13th
25. 25.What is the sum of the first 10 terms of the AP 6, 12, 18, …? (a) 660 (b) 330 (c) 360 (d) 60
26. 26.What is the sum of all the whole numbers from 1 to 50? (a) 2550 (b) 1250 (c) 1275 (d) 1225
27. 27.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 280 (b) 150 (c) 23 (d) 140
28. 28.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 42 (b) 336 (c) 168 (d) 189
29. 29.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 243 (b) 270 (c) 486 (d) 51
30. 30.What is the sum of all the whole numbers from 1 to 100? (a) 5050 (b) 10100 (c) 4950 (d) 5000
31. 31.Which term of the AP 13, 20, 27, 34, … is 83? (a) 11th (b) 12th (c) 13th (d) 10th
32. 32.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 3422 (c) 1682 (d) 1711
33. 33.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 300 (b) 276 (c) 45 (d) 552
34. 34.What is the missing term in the AP 18, ?, 22, 24, 26? (a) 19 (b) 20 (c) 22 (d) 21
35. 35.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 162 (b) 21 (c) 90 (d) 81
36. 36.What is the 24th term of the AP 13, 18, 23, 28, …? (a) 120 (b) 128 (c) 133 (d) 115
37. 37.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 380 (c) 190 (d) 37
38. 38.Which term of the AP 14, 21, 28, 35, … is 273? (a) 40th (b) 37th (c) 38th (d) 39th
39. 39.What is the 33rd term of the AP 12, 19, 26, 33, …? (a) 224 (b) 231 (c) 243 (d) 236
40. 40.What is the 17th term of the AP 11, 20, 29, 38, …? (a) 155 (b) 153 (c) 164 (d) 144

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad