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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 637 · 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 sum of the first 5 terms of the AP 7, 13, 19, …? (a) 190 (b) 110 (c) 31 (d) 95
  2. 2.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 105 (d) 210
  3. 3.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 272 (d) 256
  4. 4.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 320 (b) 580 (c) 290 (d) 56
  5. 5.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 173 (b) 39 (c) 168 (d) 336
  6. 6.What is the missing term in the AP 4, 10, 16, ?, 28? (a) 23 (b) 21 (c) 28 (d) 22
  7. 7.What is the sum of all the whole numbers from 1 to 89? (a) 4005 (b) 3916 (c) 4006 (d) 8010
  8. 8.What is the 32nd term of the AP 1, 3, 5, 7, …? (a) 63 (b) 64 (c) 62 (d) 65
  9. 9.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 684 (b) 56 (c) 372 (d) 342
  10. 10.Which term of the AP 1, 5, 9, 13, … is 73? (a) 18th (b) 19th (c) 21st (d) 20th
  11. 11.What is the sum of all the whole numbers from 1 to 14? (a) 210 (b) 91 (c) 105 (d) 98
  12. 12.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3872 (c) 7832 (d) 3916
  13. 13.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 128 (b) 72 (c) 64 (d) 15
  14. 14.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21
  15. 15.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 85 (b) 23 (c) 150 (d) 75
  16. 16.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 529 (d) 45
  17. 17.What is the missing term in the AP 16, 23, ?, 37, 44? (a) 29 (b) 30 (c) 31 (d) 37
  18. 18.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2145 (c) 2211 (d) 2178
  19. 19.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 30 (d) 9
  20. 20.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 1485 (c) 1458 (d) 2970
  21. 21.Which term of the AP 8, 11, 14, 17, … is 98? (a) 30th (b) 32nd (c) 31st (d) 33rd
  22. 22.What is the 26th term of the AP 3, 12, 21, 30, …? (a) 237 (b) 225 (c) 228 (d) 234
  23. 23.Which term of the AP 1, 8, 15, 22, … is 155? (a) 23rd (b) 25th (c) 22nd (d) 24th
  24. 24.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 105 (b) 210 (c) 114 (d) 25
  25. 25.What is the 24th term of the AP 8, 14, 20, 26, …? (a) 146 (b) 144 (c) 138 (d) 152
  26. 26.What is the missing term in the AP 6, 13, 20, ?, 34? (a) 34 (b) 27 (c) 26 (d) 28
  27. 27.What is the sum of all the whole numbers from 1 to 61? (a) 1891 (b) 1892 (c) 1830 (d) 3782
  28. 28.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 312 (b) 37 (c) 156 (d) 176
  29. 29.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 2485 (c) 5112 (d) 2557
  30. 30.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 108 (b) 120 (c) 216 (d) 24
  31. 31.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 120 (b) 114 (c) 228 (d) 15
  32. 32.What is the missing term in the AP 12, ?, 22, 27, 32? (a) 16 (b) 17 (c) 22 (d) 18
  33. 33.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 67 (c) 55 (d) 132
  34. 34.What is the missing term in the AP 1, 7, ?, 19, 25? (a) 14 (b) 13 (c) 12 (d) 19
  35. 35.What is the 10th term of the AP 9, 18, 27, 36, …? (a) 99 (b) 81 (c) 90 (d) 91
  36. 36.What is the 13th term of the AP 3, 7, 11, 15, …? (a) 52 (b) 51 (c) 55 (d) 48
  37. 37.What is the 23rd term of the AP 2, 11, 20, 29, …? (a) 198 (b) 207 (c) 209 (d) 200
  38. 38.What is the sum of all the whole numbers from 1 to 49? (a) 1226 (b) 2450 (c) 1225 (d) 1176
  39. 39.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 140 (b) 70 (c) 22 (d) 80
  40. 40.What is the 39th term of the AP 1, 5, 9, 13, …? (a) 156 (b) 152 (c) 157 (d) 153

Answer key

  1. 95
  2. 196
  3. 256
  4. 290
  5. 168
  6. 22
  7. 4005
  8. 63
  9. 342
  10. 19th
  11. 105
  12. 3916
  13. 64
  14. 121
  15. 75
  16. 529
  17. 30
  18. 2211
  19. 25
  20. 1485
  21. 31st
  22. 228
  23. 23rd
  24. 105
  25. 146
  26. 27
  27. 1891
  28. 156
  29. 2556
  30. 108
  31. 114
  32. 17
  33. 66
  34. 13
  35. 90
  36. 51
  37. 200
  38. 1225
  39. 70
  40. 153

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