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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 578 · 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 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 253 (d) 484
  2. 2.What is the 29th term of the AP 12, 16, 20, 24, …? (a) 116 (b) 112 (c) 124 (d) 128
  3. 3.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 308 (b) 24 (c) 154 (d) 165
  4. 4.What is the 15th term of the AP 15, 17, 19, 21, …? (a) 45 (b) 43 (c) 30 (d) 28
  5. 5.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 702 (d) 676
  6. 6.What is the 37th term of the AP 15, 21, 27, 33, …? (a) 216 (b) 231 (c) 237 (d) 222
  7. 7.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 9 (b) 10 (c) 12 (d) 8
  8. 8.What is the missing term in the AP 8, 14, ?, 26, 32? (a) 21 (b) 26 (c) 19 (d) 20
  9. 9.Which term of the AP 11, 18, 25, 32, … is 144? (a) 22nd (b) 19th (c) 21st (d) 20th
  10. 10.Which term of the AP 13, 18, 23, 28, … is 63? (a) 12th (b) 10th (c) 11th (d) 13th
  11. 11.What is the 18th term of the AP 18, 22, 26, 30, …? (a) 72 (b) 68 (c) 86 (d) 90
  12. 12.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 841 (c) 57 (d) 870
  13. 13.What is the 39th term of the AP 17, 23, 29, 35, …? (a) 228 (b) 234 (c) 245 (d) 251
  14. 14.Which term of the AP 4, 6, 8, 10, … is 22? (a) 9th (b) 12th (c) 10th (d) 11th
  15. 15.What is the missing term in the AP 1, 6, ?, 16, 21? (a) 12 (b) 10 (c) 11 (d) 16
  16. 16.What is the sum of the first 8 terms of the AP 3, 7, 11, …? (a) 136 (b) 31 (c) 272 (d) 152
  17. 17.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 90 (b) 27 (c) 75 (d) 150
  18. 18.Which term of the AP 2, 11, 20, 29, … is 227? (a) 25th (b) 28th (c) 27th (d) 26th
  19. 19.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 595 (c) 631 (d) 1260
  20. 20.What is the 29th term of the AP 9, 11, 13, 15, …? (a) 58 (b) 65 (c) 56 (d) 67
  21. 21.What is the sum of the first 11 terms of the AP 10, 15, 20, …? (a) 390 (b) 60 (c) 385 (d) 770
  22. 22.What is the 29th term of the AP 2, 11, 20, 29, …? (a) 252 (b) 263 (c) 261 (d) 254
  23. 23.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2850 (c) 2926 (d) 2888
  24. 24.Which term of the AP 3, 10, 17, 24, … is 248? (a) 38th (b) 37th (c) 35th (d) 36th
  25. 25.What is the 33rd term of the AP 17, 20, 23, 26, …? (a) 99 (b) 113 (c) 96 (d) 116
  26. 26.What is the 14th term of the AP 13, 18, 23, 28, …? (a) 78 (b) 83 (c) 70 (d) 65
  27. 27.What is the 16th term of the AP 10, 18, 26, 34, …? (a) 128 (b) 138 (c) 120 (d) 130
  28. 28.What is the sum of all the whole numbers from 1 to 79? (a) 6320 (b) 3161 (c) 3160 (d) 3081
  29. 29.What is the missing term in the AP 11, 13, ?, 17, 19? (a) 14 (b) 16 (c) 15 (d) 17
  30. 30.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 264 (b) 17 (c) 133 (d) 132
  31. 31.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 10 (b) 8 (c) 11 (d) 9
  32. 32.What is the 14th term of the AP 7, 13, 19, 25, …? (a) 84 (b) 78 (c) 85 (d) 91
  33. 33.Which term of the AP 9, 13, 17, 21, … is 153? (a) 36th (b) 39th (c) 38th (d) 37th
  34. 34.What is the missing term in the AP 18, 20, 22, ?, 26? (a) 23 (b) 25 (c) 24 (d) 26
  35. 35.What is the missing term in the AP 17, ?, 35, 44, 53? (a) 35 (b) 25 (c) 27 (d) 26
  36. 36.Which term of the AP 20, 28, 36, 44, … is 260? (a) 33rd (b) 31st (c) 30th (d) 32nd
  37. 37.What is the missing term in the AP 7, 14, 21, ?, 35? (a) 29 (b) 28 (c) 27 (d) 35
  38. 38.What is the missing term in the AP 8, 12, 16, ?, 24? (a) 21 (b) 20 (c) 19 (d) 24
  39. 39.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 380 (d) 361
  40. 40.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 1190 (c) 561 (d) 578

Answer key

  1. 484
  2. 124
  3. 154
  4. 43
  5. 676
  6. 231
  7. 9
  8. 20
  9. 20th
  10. 11th
  11. 86
  12. 841
  13. 245
  14. 10th
  15. 11
  16. 136
  17. 75
  18. 26th
  19. 630
  20. 65
  21. 385
  22. 254
  23. 2926
  24. 36th
  25. 113
  26. 78
  27. 130
  28. 3160
  29. 15
  30. 132
  31. 9
  32. 85
  33. 37th
  34. 24
  35. 26
  36. 31st
  37. 28
  38. 20
  39. 361
  40. 595

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