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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 333 · 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 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 784 (c) 812 (d) 406
  2. 2.What is the missing term in the AP 4, 11, 18, ?, 32? (a) 25 (b) 26 (c) 32 (d) 24
  3. 3.What is the 15th term of the AP 15, 24, 33, 42, …? (a) 135 (b) 141 (c) 150 (d) 126
  4. 4.What is the 36th term of the AP 13, 18, 23, 28, …? (a) 175 (b) 193 (c) 188 (d) 180
  5. 5.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 108 (b) 109 (c) 216 (d) 16
  6. 6.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 290 (b) 160 (c) 28 (d) 145
  7. 7.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 324 (b) 594 (c) 297 (d) 57
  8. 8.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 42 (b) 234 (c) 252 (d) 468
  9. 9.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 45 (b) 90 (c) 10 (d) 48
  10. 10.Which term of the AP 11, 14, 17, 20, … is 65? (a) 19th (b) 18th (c) 20th (d) 21st
  11. 11.What is the missing term in the AP 14, 22, ?, 38, 46? (a) 31 (b) 38 (c) 30 (d) 29
  12. 12.What is the sum of the first 12 terms of the AP 5, 8, 11, …? (a) 516 (b) 258 (c) 38 (d) 276
  13. 13.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 320 (b) 34 (c) 176 (d) 160
  14. 14.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 16 (b) 11 (c) 13 (d) 12
  15. 15.Which term of the AP 16, 22, 28, 34, … is 232? (a) 39th (b) 38th (c) 37th (d) 36th
  16. 16.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 69 (b) 468 (c) 432 (d) 864
  17. 17.What is the missing term in the AP 3, 8, ?, 18, 23? (a) 18 (b) 14 (c) 13 (d) 12
  18. 18.What is the 17th term of the AP 18, 20, 22, 24, …? (a) 50 (b) 52 (c) 32 (d) 34
  19. 19.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 182 (c) 169 (d) 91
  20. 20.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 930 (c) 465 (d) 900
  21. 21.What is the 37th term of the AP 19, 24, 29, 34, …? (a) 180 (b) 199 (c) 185 (d) 204
  22. 22.What is the 30th term of the AP 3, 6, 9, 12, …? (a) 90 (b) 91 (c) 93 (d) 87
  23. 23.What is the 29th term of the AP 3, 8, 13, 18, …? (a) 143 (b) 140 (c) 145 (d) 148
  24. 24.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 291 (b) 572 (c) 51 (d) 286
  25. 25.What is the 22nd term of the AP 9, 12, 15, 18, …? (a) 66 (b) 63 (c) 75 (d) 72
  26. 26.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 2048 (c) 4160 (d) 2080
  27. 27.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 595 (c) 578 (d) 561
  28. 28.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 153 (c) 136 (d) 154
  29. 29.What is the sum of all the whole numbers from 1 to 90? (a) 4050 (b) 4005 (c) 8190 (d) 4095
  30. 30.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 85 (b) 15 (c) 84 (d) 168
  31. 31.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4608 (c) 4656 (d) 4560
  32. 32.What is the 23rd term of the AP 11, 15, 19, 23, …? (a) 92 (b) 88 (c) 99 (d) 103
  33. 33.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 300 (d) 600
  34. 34.What is the 22nd term of the AP 4, 7, 10, 13, …? (a) 67 (b) 63 (c) 66 (d) 70
  35. 35.What is the 15th term of the AP 12, 21, 30, 39, …? (a) 147 (b) 126 (c) 135 (d) 138
  36. 36.Which term of the AP 1, 4, 7, 10, … is 112? (a) 39th (b) 37th (c) 40th (d) 38th
  37. 37.Which term of the AP 3, 7, 11, 15, … is 39? (a) 9th (b) 11th (c) 12th (d) 10th
  38. 38.What is the 23rd term of the AP 9, 14, 19, 24, …? (a) 110 (b) 115 (c) 119 (d) 124
  39. 39.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 392 (c) 378 (d) 406
  40. 40.What is the 30th term of the AP 8, 12, 16, 20, …? (a) 120 (b) 116 (c) 128 (d) 124

Answer key

  1. 784
  2. 25
  3. 141
  4. 188
  5. 108
  6. 145
  7. 297
  8. 234
  9. 45
  10. 19th
  11. 30
  12. 258
  13. 160
  14. 12
  15. 37th
  16. 432
  17. 13
  18. 50
  19. 169
  20. 900
  21. 199
  22. 90
  23. 143
  24. 286
  25. 72
  26. 2080
  27. 595
  28. 153
  29. 4095
  30. 84
  31. 4656
  32. 99
  33. 576
  34. 67
  35. 138
  36. 38th
  37. 10th
  38. 119
  39. 406
  40. 124

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