Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 836 · 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.Which term of the AP 2, 4, 6, 8, … is 26? (a) 13th (b) 14th (c) 15th (d) 12th
2. 2.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 27 (b) 190 (c) 180 (d) 360
3. 3.What is the 40th term of the AP 2, 8, 14, 20, …? (a) 236 (b) 234 (c) 240 (d) 242
4. 4.Which term of the AP 1, 9, 17, 25, … is 225? (a) 30th (b) 28th (c) 31st (d) 29th
5. 5.What is the 23rd term of the AP 17, 21, 25, 29, …? (a) 88 (b) 105 (c) 109 (d) 92
6. 6.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 42 (b) 396 (c) 198 (d) 203
7. 7.What is the 30th term of the AP 6, 12, 18, 24, …? (a) 181 (b) 180 (c) 174 (d) 186
8. 8.What is the 25th term of the AP 6, 9, 12, 15, …? (a) 75 (b) 72 (c) 78 (d) 81
9. 9.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 1711 (c) 1682 (d) 3422
10. 10.What is the missing term in the AP 16, ?, 22, 25, 28? (a) 18 (b) 20 (c) 19 (d) 22
11. 11.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 552 (b) 300 (c) 45 (d) 276
12. 12.What is the 16th term of the AP 9, 16, 23, 30, …? (a) 114 (b) 105 (c) 112 (d) 121
13. 13.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 9 (d) 25
14. 14.What is the 15th term of the AP 12, 15, 18, 21, …? (a) 57 (b) 42 (c) 45 (d) 54
15. 15.What is the 17th term of the AP 5, 9, 13, 17, …? (a) 68 (b) 64 (c) 73 (d) 69
16. 16.What is the 14th term of the AP 4, 8, 12, 16, …? (a) 60 (b) 57 (c) 52 (d) 56
17. 17.What is the 28th term of the AP 4, 11, 18, 25, …? (a) 189 (b) 200 (c) 193 (d) 196
18. 18.What is the 35th term of the AP 14, 19, 24, 29, …? (a) 175 (b) 170 (c) 184 (d) 189
19. 19.What is the 37th term of the AP 2, 11, 20, 29, …? (a) 335 (b) 326 (c) 324 (d) 333
20. 20.What is the missing term in the AP 1, 4, 7, ?, 13? (a) 10 (b) 9 (c) 11 (d) 13
21. 21.What is the 11th term of the AP 1, 5, 9, 13, …? (a) 40 (b) 44 (c) 45 (d) 41
22. 22.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 49 (c) 13 (d) 56
23. 23.What is the 25th term of the AP 11, 13, 15, 17, …? (a) 61 (b) 59 (c) 50 (d) 48
24. 24.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 15 (d) 72
25. 25.What is the sum of all the whole numbers from 1 to 51? (a) 1275 (b) 2652 (c) 1327 (d) 1326
26. 26.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 23 (b) 19 (c) 20 (d) 18
27. 27.What is the 16th term of the AP 6, 14, 22, 30, …? (a) 134 (b) 128 (c) 126 (d) 120
28. 28.What is the 18th term of the AP 20, 23, 26, 29, …? (a) 54 (b) 74 (c) 51 (d) 71
29. 29.What is the 38th term of the AP 10, 14, 18, 22, …? (a) 162 (b) 148 (c) 152 (d) 158
30. 30.Which term of the AP 16, 24, 32, 40, … is 248? (a) 29th (b) 31st (c) 32nd (d) 30th
31. 31.What is the 24th term of the AP 19, 25, 31, 37, …? (a) 157 (b) 138 (c) 144 (d) 163
32. 32.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 18 (b) 120 (c) 60 (d) 63
33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 66 (d) 132
34. 34.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 1190 (c) 578 (d) 595
35. 35.What is the 28th term of the AP 20, 29, 38, 47, …? (a) 272 (b) 243 (c) 263 (d) 252
36. 36.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 60 (b) 12 (c) 114 (d) 57
37. 37.What is the 25th term of the AP 1, 10, 19, 28, …? (a) 225 (b) 217 (c) 226 (d) 216
38. 38.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 40 (b) 35 (c) 70 (d) 11
39. 39.Which term of the AP 8, 14, 20, 26, … is 176? (a) 30th (b) 29th (c) 28th (d) 31st
40. 40.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 126 (b) 64 (c) 11 (d) 63

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