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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 4 · 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 37th term of the AP 10, 19, 28, 37, …? (a) 333 (b) 324 (c) 343 (d) 334
  2. 2.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 72 (b) 42 (c) 36 (d) 11
  3. 3.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 308 (b) 46 (c) 572 (d) 286
  4. 4.What is the 23rd term of the AP 15, 22, 29, 36, …? (a) 169 (b) 154 (c) 176 (d) 161
  5. 5.What is the 15th term of the AP 4, 6, 8, 10, …? (a) 34 (b) 32 (c) 28 (d) 30
  6. 6.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 722 (c) 703 (d) 1482
  7. 7.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 14 (b) 108 (c) 60 (d) 54
  8. 8.Which term of the AP 6, 12, 18, 24, … is 126? (a) 20th (b) 22nd (c) 21st (d) 23rd
  9. 9.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 35 (b) 70 (c) 9 (d) 36
  10. 10.What is the 11th term of the AP 13, 17, 21, 25, …? (a) 44 (b) 40 (c) 57 (d) 53
  11. 11.What is the missing term in the AP 2, 4, 6, ?, 10? (a) 8 (b) 10 (c) 9 (d) 7
  12. 12.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 426 (b) 63 (c) 456 (d) 852
  13. 13.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 47 (c) 300 (d) 576
  14. 14.Which term of the AP 19, 23, 27, 31, … is 119? (a) 27th (b) 28th (c) 25th (d) 26th
  15. 15.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 595 (c) 630 (d) 1260
  16. 16.What is the 13th term of the AP 16, 23, 30, 37, …? (a) 100 (b) 107 (c) 84 (d) 91
  17. 17.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 132 (b) 143 (c) 22 (d) 264
  18. 18.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 171 (c) 342 (d) 153
  19. 19.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 21 (b) 81 (c) 90 (d) 162
  20. 20.What is the missing term in the AP 15, 24, ?, 42, 51? (a) 32 (b) 42 (c) 33 (d) 34
  21. 21.What is the 12th term of the AP 18, 20, 22, 24, …? (a) 24 (b) 40 (c) 22 (d) 42
  22. 22.What is the 32nd term of the AP 12, 16, 20, 24, …? (a) 128 (b) 124 (c) 140 (d) 136
  23. 23.What is the 39th term of the AP 6, 9, 12, 15, …? (a) 114 (b) 120 (c) 117 (d) 123
  24. 24.What is the 36th term of the AP 6, 14, 22, 30, …? (a) 286 (b) 294 (c) 288 (d) 280
  25. 25.Which term of the AP 6, 14, 22, 30, … is 222? (a) 30th (b) 29th (c) 28th (d) 27th
  26. 26.Which term of the AP 1, 5, 9, 13, … is 133? (a) 35th (b) 36th (c) 33rd (d) 34th
  27. 27.What is the 15th term of the AP 8, 11, 14, 17, …? (a) 45 (b) 50 (c) 42 (d) 53
  28. 28.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 441 (c) 231 (d) 41
  29. 29.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 42 (b) 196 (c) 216 (d) 392
  30. 30.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 300 (b) 282 (c) 564 (d) 40
  31. 31.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 136 (c) 306 (d) 154
  32. 32.What is the 22nd term of the AP 2, 4, 6, 8, …? (a) 46 (b) 45 (c) 42 (d) 44
  33. 33.What is the 27th term of the AP 3, 7, 11, 15, …? (a) 108 (b) 111 (c) 107 (d) 104
  34. 34.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 306 (d) 289
  35. 35.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 160 (b) 34 (c) 176 (d) 320
  36. 36.What is the 11th term of the AP 7, 9, 11, 13, …? (a) 20 (b) 22 (c) 27 (d) 29
  37. 37.Which term of the AP 6, 11, 16, 21, … is 141? (a) 30th (b) 29th (c) 27th (d) 28th
  38. 38.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 1128 (c) 1081 (d) 2256
  39. 39.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 19 (b) 23 (c) 20 (d) 21
  40. 40.Which term of the AP 17, 20, 23, 26, … is 71? (a) 20th (b) 18th (c) 19th (d) 21st

Answer key

  1. 334
  2. 36
  3. 286
  4. 169
  5. 32
  6. 741
  7. 54
  8. 21st
  9. 35
  10. 53
  11. 8
  12. 426
  13. 576
  14. 26th
  15. 630
  16. 100
  17. 132
  18. 171
  19. 81
  20. 33
  21. 40
  22. 136
  23. 120
  24. 286
  25. 28th
  26. 34th
  27. 50
  28. 441
  29. 196
  30. 282
  31. 153
  32. 44
  33. 107
  34. 289
  35. 160
  36. 27
  37. 28th
  38. 1128
  39. 20
  40. 19th

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