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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 830 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.What is the 13th term of the AP 4, 7, 10, 13, …? (a) 43 (b) 36 (c) 39 (d) 40
  2. 2.Which term of the AP 4, 12, 20, 28, … is 60? (a) 8th (b) 9th (c) 7th (d) 10th
  3. 3.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 841 (d) 870
  4. 4.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 187 (b) 374 (c) 190 (d) 32
  5. 5.What is the 39th term of the AP 14, 22, 30, 38, …? (a) 312 (b) 304 (c) 318 (d) 326
  6. 6.What is the 18th term of the AP 6, 13, 20, 27, …? (a) 119 (b) 132 (c) 125 (d) 126
  7. 7.What is the 38th term of the AP 5, 13, 21, 29, …? (a) 301 (b) 304 (c) 309 (d) 296
  8. 8.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 324 (b) 34 (c) 180 (d) 162
  9. 9.What is the 10th term of the AP 3, 10, 17, 24, …? (a) 63 (b) 70 (c) 73 (d) 66
  10. 10.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 21 (b) 28 (c) 20 (d) 22
  11. 11.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 594 (b) 47 (c) 297 (d) 319
  12. 12.What is the 22nd term of the AP 17, 21, 25, 29, …? (a) 88 (b) 84 (c) 101 (d) 105
  13. 13.What is the 10th term of the AP 5, 7, 9, 11, …? (a) 23 (b) 20 (c) 18 (d) 25
  14. 14.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 465 (c) 930 (d) 59
  15. 15.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 572 (b) 51 (c) 291 (d) 286
  16. 16.What is the missing term in the AP 14, 16, ?, 20, 22? (a) 19 (b) 20 (c) 17 (d) 18
  17. 17.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 1980 (c) 968 (d) 946
  18. 18.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 13 (b) 11 (c) 12 (d) 17
  19. 19.What is the 32nd term of the AP 1, 6, 11, 16, …? (a) 155 (b) 161 (c) 156 (d) 160
  20. 20.Which term of the AP 19, 21, 23, 25, … is 89? (a) 36th (b) 35th (c) 38th (d) 37th
  21. 21.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 8 (b) 7 (c) 9 (d) 6
  22. 22.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 56 (b) 14 (c) 63 (d) 112
  23. 23.What is the 27th term of the AP 12, 18, 24, 30, …? (a) 162 (b) 156 (c) 168 (d) 174
  24. 24.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 14 (b) 10 (c) 11 (d) 12
  25. 25.What is the 28th term of the AP 10, 13, 16, 19, …? (a) 81 (b) 84 (c) 94 (d) 91
  26. 26.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 144 (b) 153 (c) 24 (d) 288
  27. 27.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 4160 (c) 2016 (d) 2080
  28. 28.What is the missing term in the AP 5, 8, 11, ?, 17? (a) 17 (b) 14 (c) 13 (d) 15
  29. 29.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 180 (b) 13 (c) 96 (d) 90
  30. 30.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 336 (b) 50 (c) 672 (d) 360
  31. 31.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 4851 (c) 9900 (d) 4951
  32. 32.What is the 38th term of the AP 20, 23, 26, 29, …? (a) 111 (b) 134 (c) 114 (d) 131
  33. 33.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 38 (b) 164 (c) 328 (d) 184
  34. 34.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 215 (b) 35 (c) 230 (d) 430
  35. 35.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 28 (c) 56 (d) 13
  36. 36.What is the 25th term of the AP 14, 20, 26, 32, …? (a) 164 (b) 158 (c) 150 (d) 144
  37. 37.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 276 (c) 600 (d) 300
  38. 38.What is the 13th term of the AP 2, 11, 20, 29, …? (a) 117 (b) 119 (c) 110 (d) 108
  39. 39.What is the 21st term of the AP 11, 14, 17, 20, …? (a) 63 (b) 71 (c) 60 (d) 74
  40. 40.What is the sum of all the whole numbers from 1 to 30? (a) 465 (b) 930 (c) 435 (d) 450

Answer key

  1. 40
  2. 8th
  3. 841
  4. 187
  5. 318
  6. 125
  7. 301
  8. 162
  9. 66
  10. 21
  11. 297
  12. 101
  13. 23
  14. 900
  15. 286
  16. 18
  17. 990
  18. 12
  19. 156
  20. 36th
  21. 7
  22. 56
  23. 168
  24. 11
  25. 91
  26. 144
  27. 2080
  28. 14
  29. 90
  30. 336
  31. 4950
  32. 131
  33. 164
  34. 215
  35. 49
  36. 158
  37. 300
  38. 110
  39. 71
  40. 465

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