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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 278 · 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 all the whole numbers from 1 to 54? (a) 2970 (b) 1458 (c) 1431 (d) 1485
  2. 2.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 465 (c) 497 (d) 496
  3. 3.What is the 21st term of the AP 7, 14, 21, 28, …? (a) 154 (b) 140 (c) 148 (d) 147
  4. 4.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 17 (b) 276 (c) 144 (d) 138
  5. 5.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 33 (b) 153 (c) 306 (d) 171
  6. 6.What is the missing term in the AP 7, 14, ?, 28, 35? (a) 20 (b) 28 (c) 21 (d) 22
  7. 7.What is the missing term in the AP 6, 9, 12, ?, 18? (a) 14 (b) 18 (c) 16 (d) 15
  8. 8.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 1226 (c) 2450 (d) 1176
  9. 9.What is the sum of the first 8 terms of the AP 4, 8, 12, …? (a) 160 (b) 32 (c) 144 (d) 288
  10. 10.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 578 (c) 595 (d) 1190
  11. 11.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 29 (b) 95 (c) 190 (d) 100
  12. 12.What is the 13th term of the AP 11, 13, 15, 17, …? (a) 35 (b) 24 (c) 37 (d) 26
  13. 13.Which term of the AP 2, 7, 12, 17, … is 132? (a) 27th (b) 28th (c) 29th (d) 26th
  14. 14.What is the sum of all the whole numbers from 1 to 92? (a) 4186 (b) 8556 (c) 4278 (d) 4232
  15. 15.What is the 21st term of the AP 13, 19, 25, 31, …? (a) 120 (b) 126 (c) 139 (d) 133
  16. 16.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 17 (b) 118 (c) 234 (d) 117
  17. 17.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 384 (b) 354 (c) 708 (d) 57
  18. 18.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 26 (b) 81 (c) 96 (d) 162
  19. 19.What is the 38th term of the AP 4, 12, 20, 28, …? (a) 304 (b) 308 (c) 300 (d) 296
  20. 20.What is the missing term in the AP 18, 21, 24, ?, 30? (a) 26 (b) 27 (c) 30 (d) 28
  21. 21.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 361 (c) 37 (d) 380
  22. 22.What is the 33rd term of the AP 13, 21, 29, 37, …? (a) 277 (b) 269 (c) 264 (d) 256
  23. 23.What is the sum of all the whole numbers from 1 to 13? (a) 92 (b) 91 (c) 182 (d) 78
  24. 24.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 12 (b) 48 (c) 84 (d) 42
  25. 25.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 465 (c) 900 (d) 59
  26. 26.What is the 32nd term of the AP 15, 18, 21, 24, …? (a) 96 (b) 93 (c) 111 (d) 108
  27. 27.What is the missing term in the AP 20, ?, 30, 35, 40? (a) 26 (b) 24 (c) 30 (d) 25
  28. 28.Which term of the AP 14, 20, 26, 32, … is 86? (a) 12th (b) 14th (c) 15th (d) 13th
  29. 29.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 192 (b) 104 (c) 19 (d) 96
  30. 30.What is the missing term in the AP 14, 23, 32, ?, 50? (a) 42 (b) 40 (c) 41 (d) 50
  31. 31.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 120 (b) 105 (c) 30 (d) 210
  32. 32.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 153 (c) 289 (d) 33
  33. 33.What is the 32nd term of the AP 17, 24, 31, 38, …? (a) 217 (b) 234 (c) 241 (d) 224
  34. 34.Which term of the AP 11, 17, 23, 29, … is 137? (a) 21st (b) 23rd (c) 24th (d) 22nd
  35. 35.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 31 (b) 114 (c) 192 (d) 96
  36. 36.What is the 14th term of the AP 11, 14, 17, 20, …? (a) 50 (b) 42 (c) 53 (d) 39
  37. 37.What is the 23rd term of the AP 2, 10, 18, 26, …? (a) 186 (b) 176 (c) 184 (d) 178
  38. 38.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 4656 (c) 4560 (d) 9312
  39. 39.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 144 (d) 78
  40. 40.What is the missing term in the AP 19, 27, ?, 43, 51? (a) 43 (b) 34 (c) 35 (d) 36

Answer key

  1. 1485
  2. 496
  3. 147
  4. 138
  5. 153
  6. 21
  7. 15
  8. 1225
  9. 144
  10. 595
  11. 95
  12. 35
  13. 27th
  14. 4278
  15. 133
  16. 117
  17. 354
  18. 81
  19. 300
  20. 27
  21. 361
  22. 269
  23. 91
  24. 42
  25. 900
  26. 108
  27. 25
  28. 13th
  29. 96
  30. 41
  31. 105
  32. 289
  33. 234
  34. 22nd
  35. 96
  36. 50
  37. 178
  38. 4656
  39. 144
  40. 35

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