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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 627 · 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 50? (a) 2550 (b) 1275 (c) 1225 (d) 1250
  2. 2.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 28 (d) 49
  3. 3.What is the sum of all the whole numbers from 1 to 70? (a) 4970 (b) 2415 (c) 2485 (d) 2450
  4. 4.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 65 (b) 25 (c) 130 (d) 80
  5. 5.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 22 (b) 26 (c) 23 (d) 24
  6. 6.What is the sum of the first 10 terms of the AP 4, 10, 16, …? (a) 58 (b) 620 (c) 310 (d) 340
  7. 7.What is the 16th term of the AP 16, 18, 20, 22, …? (a) 32 (b) 48 (c) 30 (d) 46
  8. 8.What is the sum of the first 9 terms of the AP 6, 11, 16, …? (a) 239 (b) 234 (c) 46 (d) 468
  9. 9.What is the 30th term of the AP 18, 22, 26, 30, …? (a) 116 (b) 134 (c) 138 (d) 120
  10. 10.What is the sum of the first 10 terms of the AP 7, 12, 17, …? (a) 52 (b) 590 (c) 320 (d) 295
  11. 11.Which term of the AP 15, 20, 25, 30, … is 65? (a) 13th (b) 12th (c) 11th (d) 10th
  12. 12.What is the 36th term of the AP 14, 22, 30, 38, …? (a) 294 (b) 288 (c) 280 (d) 302
  13. 13.What is the 39th term of the AP 14, 22, 30, 38, …? (a) 304 (b) 326 (c) 318 (d) 312
  14. 14.What is the missing term in the AP 15, 22, 29, ?, 43? (a) 35 (b) 37 (c) 36 (d) 43
  15. 15.What is the sum of the first 11 terms of the AP 10, 16, 22, …? (a) 880 (b) 70 (c) 440 (d) 473
  16. 16.What is the 30th term of the AP 2, 6, 10, 14, …? (a) 122 (b) 120 (c) 118 (d) 116
  17. 17.Which term of the AP 14, 19, 24, 29, … is 169? (a) 31st (b) 32nd (c) 33rd (d) 34th
  18. 18.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 18 (b) 11 (c) 12 (d) 13
  19. 19.What is the sum of all the whole numbers from 1 to 39? (a) 1560 (b) 780 (c) 741 (d) 781
  20. 20.What is the 34th term of the AP 1, 3, 5, 7, …? (a) 69 (b) 68 (c) 67 (d) 66
  21. 21.What is the missing term in the AP 11, 20, ?, 38, 47? (a) 38 (b) 28 (c) 30 (d) 29
  22. 22.What is the 28th term of the AP 13, 19, 25, 31, …? (a) 175 (b) 162 (c) 168 (d) 181
  23. 23.Which term of the AP 16, 24, 32, 40, … is 312? (a) 38th (b) 37th (c) 40th (d) 39th
  24. 24.Which term of the AP 15, 22, 29, 36, … is 155? (a) 20th (b) 23rd (c) 21st (d) 22nd
  25. 25.Which term of the AP 19, 25, 31, 37, … is 253? (a) 41st (b) 40th (c) 42nd (d) 39th
  26. 26.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 594 (b) 302 (c) 52 (d) 297
  27. 27.What is the sum of all the whole numbers from 1 to 95? (a) 4560 (b) 4465 (c) 4561 (d) 9120
  28. 28.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 253 (d) 484
  29. 29.What is the sum of all the whole numbers from 1 to 27? (a) 756 (b) 379 (c) 351 (d) 378
  30. 30.What is the 39th term of the AP 10, 16, 22, 28, …? (a) 244 (b) 228 (c) 234 (d) 238
  31. 31.What is the 13th term of the AP 15, 23, 31, 39, …? (a) 96 (b) 119 (c) 104 (d) 111
  32. 32.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 196 (c) 27 (d) 105
  33. 33.What is the 37th term of the AP 1, 7, 13, 19, …? (a) 217 (b) 216 (c) 223 (d) 222
  34. 34.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 136 (c) 256 (d) 272
  35. 35.What is the 22nd term of the AP 7, 9, 11, 13, …? (a) 42 (b) 51 (c) 49 (d) 44
  36. 36.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 8 (b) 6 (c) 12 (d) 7
  37. 37.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 56 (b) 52 (c) 10 (d) 104
  38. 38.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 1980 (c) 968 (d) 990
  39. 39.What is the sum of all the whole numbers from 1 to 89? (a) 8010 (b) 4005 (c) 4006 (d) 3916
  40. 40.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 17 (d) 90

Answer key

  1. 1275
  2. 49
  3. 2485
  4. 65
  5. 23
  6. 310
  7. 46
  8. 234
  9. 134
  10. 295
  11. 11th
  12. 294
  13. 318
  14. 36
  15. 440
  16. 118
  17. 32nd
  18. 12
  19. 780
  20. 67
  21. 29
  22. 175
  23. 38th
  24. 21st
  25. 40th
  26. 297
  27. 4560
  28. 484
  29. 378
  30. 238
  31. 111
  32. 196
  33. 217
  34. 256
  35. 49
  36. 7
  37. 52
  38. 990
  39. 4005
  40. 81

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