Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 95 · 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 12 terms of the AP 8, 9, 10, …? (a) 19 (b) 168 (c) 162 (d) 324
2. 2.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 272 (b) 136 (c) 24 (d) 144
3. 3.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 67 (c) 132 (d) 55
4. 4.What is the missing term in the AP 15, 22, 29, ?, 43? (a) 43 (b) 36 (c) 37 (d) 35
5. 5.What is the missing term in the AP 12, 17, 22, ?, 32? (a) 28 (b) 32 (c) 26 (d) 27
6. 6.What is the 30th term of the AP 2, 6, 10, 14, …? (a) 116 (b) 122 (c) 118 (d) 120
7. 7.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 441 (d) 41
8. 8.Which term of the AP 5, 10, 15, 20, … is 95? (a) 21st (b) 20th (c) 18th (d) 19th
9. 9.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 90 (b) 81 (c) 162 (d) 21
10. 10.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 198 (b) 108 (c) 19 (d) 99
11. 11.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 2756 (c) 1326 (d) 1378
12. 12.What is the 31st term of the AP 17, 24, 31, 38, …? (a) 227 (b) 217 (c) 210 (d) 234
13. 13.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 140 (b) 70 (c) 73 (d) 20
14. 14.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 28 (b) 21 (c) 22 (d) 20
15. 15.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 40 (b) 175 (c) 180 (d) 350
16. 16.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 7 (b) 5 (c) 6 (d) 10
17. 17.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 90 (b) 27 (c) 85 (d) 170
18. 18.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 20 (b) 330 (c) 165 (d) 166
19. 19.What is the 24th term of the AP 11, 14, 17, 20, …? (a) 69 (b) 80 (c) 72 (d) 83
20. 20.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 2145 (c) 2211 (d) 4422
21. 21.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 43 (b) 352 (c) 176 (d) 200
22. 22.What is the missing term in the AP 14, 23, 32, ?, 50? (a) 40 (b) 50 (c) 41 (d) 42
23. 23.What is the 26th term of the AP 18, 23, 28, 33, …? (a) 125 (b) 130 (c) 143 (d) 148
24. 24.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 14 (b) 15 (c) 18 (d) 16
25. 25.What is the 31st term of the AP 10, 19, 28, 37, …? (a) 280 (b) 270 (c) 279 (d) 289
26. 26.What is the 22nd term of the AP 2, 7, 12, 17, …? (a) 110 (b) 112 (c) 105 (d) 107
27. 27.What is the 30th term of the AP 3, 12, 21, 30, …? (a) 273 (b) 261 (c) 270 (d) 264
28. 28.What is the 29th term of the AP 2, 10, 18, 26, …? (a) 224 (b) 226 (c) 232 (d) 234
29. 29.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 121 (c) 21 (d) 66
30. 30.Which term of the AP 3, 10, 17, 24, … is 129? (a) 20th (b) 18th (c) 19th (d) 21st
31. 31.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 14 (b) 12 (c) 16 (d) 13
32. 32.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 42 (d) 21
33. 33.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 171 (c) 342 (d) 35
34. 34.What is the sum of the first 10 terms of the AP 6, 12, 18, …? (a) 60 (b) 360 (c) 330 (d) 660
35. 35.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 186 (b) 108 (c) 28 (d) 93
36. 36.What is the sum of all the whole numbers from 1 to 37? (a) 1406 (b) 703 (c) 704 (d) 666
37. 37.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 37 (b) 150 (c) 132 (d) 264
38. 38.What is the 13th term of the AP 5, 10, 15, 20, …? (a) 70 (b) 66 (c) 60 (d) 65
39. 39.Which term of the AP 4, 12, 20, 28, … is 252? (a) 33rd (b) 31st (c) 32nd (d) 34th
40. 40.Which term of the AP 6, 15, 24, 33, … is 105? (a) 14th (b) 12th (c) 13th (d) 11th

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