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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 234 · 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 14th term of the AP 17, 23, 29, 35, …? (a) 95 (b) 78 (c) 84 (d) 101
  2. 2.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 20 (b) 220 (c) 110 (d) 120
  3. 3.What is the 16th term of the AP 6, 10, 14, 18, …? (a) 70 (b) 66 (c) 60 (d) 64
  4. 4.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 930 (d) 900
  5. 5.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 4418 (c) 8930 (d) 4371
  6. 6.What is the 10th term of the AP 12, 17, 22, 27, …? (a) 62 (b) 45 (c) 57 (d) 50
  7. 7.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 78 (c) 92 (d) 91
  8. 8.What is the 25th term of the AP 20, 28, 36, 44, …? (a) 192 (b) 212 (c) 200 (d) 220
  9. 9.What is the 14th term of the AP 15, 21, 27, 33, …? (a) 78 (b) 93 (c) 84 (d) 99
  10. 10.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 91 (b) 182 (c) 22 (d) 94
  11. 11.What is the missing term in the AP 2, 6, 10, ?, 18? (a) 15 (b) 13 (c) 18 (d) 14
  12. 12.What is the missing term in the AP 5, ?, 19, 26, 33? (a) 13 (b) 11 (c) 19 (d) 12
  13. 13.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 17 (b) 72 (c) 144 (d) 78
  14. 14.What is the 11th term of the AP 6, 11, 16, 21, …? (a) 55 (b) 56 (c) 61 (d) 50
  15. 15.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 45 (c) 110 (d) 50
  16. 16.What is the missing term in the AP 19, ?, 37, 46, 55? (a) 29 (b) 27 (c) 28 (d) 37
  17. 17.What is the 21st term of the AP 12, 18, 24, 30, …? (a) 120 (b) 132 (c) 138 (d) 126
  18. 18.What is the 40th term of the AP 6, 11, 16, 21, …? (a) 201 (b) 200 (c) 195 (d) 206
  19. 19.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 50 (b) 7 (c) 25 (d) 26
  20. 20.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 408 (b) 204 (c) 216 (d) 28
  21. 21.Which term of the AP 11, 17, 23, 29, … is 245? (a) 39th (b) 40th (c) 41st (d) 42nd
  22. 22.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 380 (c) 171 (d) 190
  23. 23.What is the 35th term of the AP 18, 21, 24, 27, …? (a) 120 (b) 123 (c) 105 (d) 102
  24. 24.Which term of the AP 17, 25, 33, 41, … is 329? (a) 42nd (b) 40th (c) 41st (d) 39th
  25. 25.Which term of the AP 2, 5, 8, 11, … is 80? (a) 26th (b) 28th (c) 29th (d) 27th
  26. 26.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 5 (b) 4 (c) 7 (d) 6
  27. 27.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 1260 (c) 595 (d) 631
  28. 28.What is the 22nd term of the AP 1, 9, 17, 25, …? (a) 168 (b) 169 (c) 176 (d) 177
  29. 29.Which term of the AP 11, 19, 27, 35, … is 179? (a) 23rd (b) 21st (c) 24th (d) 22nd
  30. 30.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 210 (d) 196
  31. 31.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 420 (b) 210 (c) 34 (d) 228
  32. 32.What is the 12th term of the AP 11, 14, 17, 20, …? (a) 36 (b) 33 (c) 44 (d) 47
  33. 33.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 630 (b) 315 (c) 340 (d) 54
  34. 34.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 406 (c) 435 (d) 870
  35. 35.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 2556 (c) 5256 (d) 2628
  36. 36.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 346 (b) 682 (c) 56 (d) 341
  37. 37.What is the 37th term of the AP 3, 7, 11, 15, …? (a) 148 (b) 151 (c) 144 (d) 147
  38. 38.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
  39. 39.Which term of the AP 19, 22, 25, 28, … is 49? (a) 10th (b) 11th (c) 13th (d) 12th
  40. 40.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 153 (c) 154 (d) 306

Answer key

  1. 95
  2. 110
  3. 66
  4. 900
  5. 4465
  6. 57
  7. 91
  8. 212
  9. 93
  10. 91
  11. 14
  12. 12
  13. 72
  14. 56
  15. 55
  16. 28
  17. 132
  18. 201
  19. 25
  20. 204
  21. 40th
  22. 190
  23. 120
  24. 40th
  25. 27th
  26. 5
  27. 630
  28. 169
  29. 22nd
  30. 196
  31. 210
  32. 44
  33. 315
  34. 435
  35. 2628
  36. 341
  37. 147
  38. 100
  39. 11th
  40. 153

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