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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 143 · 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 11 terms of the AP 7, 9, 11, …? (a) 198 (b) 374 (c) 187 (d) 27
  2. 2.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 154 (b) 77 (c) 20 (d) 80
  3. 3.What is the missing term in the AP 20, 28, ?, 44, 52? (a) 44 (b) 36 (c) 35 (d) 37
  4. 4.Which term of the AP 1, 5, 9, 13, … is 133? (a) 34th (b) 36th (c) 33rd (d) 35th
  5. 5.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 216 (b) 120 (c) 108 (d) 24
  6. 6.What is the 30th term of the AP 1, 8, 15, 22, …? (a) 210 (b) 203 (c) 204 (d) 211
  7. 7.What is the 17th term of the AP 5, 12, 19, 26, …? (a) 112 (b) 119 (c) 124 (d) 117
  8. 8.What is the 18th term of the AP 17, 23, 29, 35, …? (a) 108 (b) 125 (c) 119 (d) 102
  9. 9.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9
  10. 10.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 72 (c) 156 (d) 78
  11. 11.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 572 (b) 291 (c) 286 (d) 51
  12. 12.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 20 (b) 18 (c) 21 (d) 19
  13. 13.What is the 12th term of the AP 3, 9, 15, 21, …? (a) 75 (b) 72 (c) 69 (d) 66
  14. 14.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 15 (c) 64 (d) 36
  15. 15.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 968 (c) 990 (d) 946
  16. 16.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 182 (c) 91 (d) 169
  17. 17.What is the 29th term of the AP 13, 22, 31, 40, …? (a) 265 (b) 274 (c) 252 (d) 261
  18. 18.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 210 (c) 105 (d) 91
  19. 19.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 121 (c) 105 (d) 120
  20. 20.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 144 (c) 23 (d) 78
  21. 21.What is the 38th term of the AP 13, 17, 21, 25, …? (a) 165 (b) 161 (c) 152 (d) 148
  22. 22.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 75 (b) 540 (c) 504 (d) 1008
  23. 23.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 50 (b) 464 (c) 256 (d) 232
  24. 24.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 435 (c) 870 (d) 57
  25. 25.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 40 (b) 20 (c) 6 (d) 21
  26. 26.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 75 (b) 18 (c) 70 (d) 140
  27. 27.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 484 (c) 253 (d) 43
  28. 28.What is the missing term in the AP 18, 22, ?, 30, 34? (a) 27 (b) 26 (c) 30 (d) 25
  29. 29.Which term of the AP 4, 13, 22, 31, … is 247? (a) 30th (b) 29th (c) 27th (d) 28th
  30. 30.What is the 18th term of the AP 1, 3, 5, 7, …? (a) 36 (b) 34 (c) 35 (d) 37
  31. 31.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 47 (c) 300 (d) 600
  32. 32.What is the 32nd term of the AP 9, 13, 17, 21, …? (a) 124 (b) 137 (c) 128 (d) 133
  33. 33.What is the 31st term of the AP 5, 9, 13, 17, …? (a) 129 (b) 124 (c) 125 (d) 120
  34. 34.What is the 37th term of the AP 3, 10, 17, 24, …? (a) 262 (b) 252 (c) 259 (d) 255
  35. 35.Which term of the AP 15, 17, 19, 21, … is 43? (a) 14th (b) 16th (c) 17th (d) 15th
  36. 36.Which term of the AP 13, 19, 25, 31, … is 67? (a) 10th (b) 12th (c) 9th (d) 11th
  37. 37.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 48 (b) 13 (c) 54 (d) 96
  38. 38.What is the missing term in the AP 17, ?, 25, 29, 33? (a) 20 (b) 25 (c) 21 (d) 22
  39. 39.What is the 15th term of the AP 4, 8, 12, 16, …? (a) 64 (b) 56 (c) 61 (d) 60
  40. 40.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 64 (b) 72 (c) 15 (d) 128

Answer key

  1. 187
  2. 77
  3. 36
  4. 34th
  5. 108
  6. 204
  7. 117
  8. 119
  9. 25
  10. 78
  11. 286
  12. 19
  13. 69
  14. 64
  15. 990
  16. 169
  17. 265
  18. 105
  19. 120
  20. 144
  21. 161
  22. 504
  23. 232
  24. 841
  25. 20
  26. 70
  27. 484
  28. 26
  29. 28th
  30. 35
  31. 576
  32. 133
  33. 125
  34. 255
  35. 15th
  36. 10th
  37. 48
  38. 21
  39. 60
  40. 64

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