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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 656 · 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 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 240 (c) 120 (d) 29
  2. 2.What is the 36th term of the AP 16, 24, 32, 40, …? (a) 296 (b) 304 (c) 280 (d) 288
  3. 3.What is the missing term in the AP 17, ?, 29, 35, 41? (a) 24 (b) 29 (c) 22 (d) 23
  4. 4.Which term of the AP 2, 4, 6, 8, … is 66? (a) 34th (b) 33rd (c) 35th (d) 32nd
  5. 5.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 3540 (c) 1770 (d) 1711
  6. 6.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 252 (b) 42 (c) 234 (d) 468
  7. 7.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 182 (c) 25 (d) 91
  8. 8.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 2256 (c) 1129 (d) 1128
  9. 9.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 78 (d) 144
  10. 10.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 5256 (c) 2628 (d) 2556
  11. 11.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 20 (b) 18 (c) 19 (d) 26
  12. 12.What is the missing term in the AP 2, 6, 10, ?, 18? (a) 15 (b) 14 (c) 13 (d) 18
  13. 13.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 105 (c) 196 (d) 27
  14. 14.Which term of the AP 2, 4, 6, 8, … is 22? (a) 11th (b) 12th (c) 13th (d) 10th
  15. 15.What is the 30th term of the AP 14, 19, 24, 29, …? (a) 159 (b) 164 (c) 150 (d) 145
  16. 16.Which term of the AP 13, 15, 17, 19, … is 81? (a) 35th (b) 36th (c) 34th (d) 37th
  17. 17.What is the 10th term of the AP 7, 11, 15, 19, …? (a) 43 (b) 36 (c) 47 (d) 40
  18. 18.What is the missing term in the AP 20, 27, ?, 41, 48? (a) 34 (b) 33 (c) 35 (d) 41
  19. 19.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 11 (b) 10 (c) 9 (d) 12
  20. 20.What is the 40th term of the AP 15, 18, 21, 24, …? (a) 135 (b) 117 (c) 120 (d) 132
  21. 21.Which term of the AP 7, 9, 11, 13, … is 31? (a) 12th (b) 14th (c) 15th (d) 13th
  22. 22.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 550 (b) 40 (c) 278 (d) 275
  23. 23.What is the 30th term of the AP 10, 16, 22, 28, …? (a) 180 (b) 190 (c) 174 (d) 184
  24. 24.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 140 (b) 73 (c) 20 (d) 70
  25. 25.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 257 (b) 252 (c) 504 (d) 48
  26. 26.What is the sum of all the whole numbers from 1 to 37? (a) 704 (b) 703 (c) 1406 (d) 666
  27. 27.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 42 (b) 392 (c) 196 (d) 216
  28. 28.What is the 15th term of the AP 20, 22, 24, 26, …? (a) 30 (b) 28 (c) 50 (d) 48
  29. 29.What is the 10th term of the AP 6, 9, 12, 15, …? (a) 27 (b) 36 (c) 33 (d) 30
  30. 30.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 248 (b) 486 (c) 243 (d) 47
  31. 31.What is the 29th term of the AP 10, 18, 26, 34, …? (a) 234 (b) 232 (c) 242 (d) 224
  32. 32.Which term of the AP 17, 22, 27, 32, … is 52? (a) 8th (b) 7th (c) 10th (d) 9th
  33. 33.What is the 24th term of the AP 11, 14, 17, 20, …? (a) 83 (b) 72 (c) 69 (d) 80
  34. 34.What is the sum of all the whole numbers from 1 to 73? (a) 5402 (b) 2701 (c) 2628 (d) 2702
  35. 35.What is the 21st term of the AP 19, 21, 23, 25, …? (a) 42 (b) 40 (c) 59 (d) 61
  36. 36.What is the 35th term of the AP 13, 20, 27, 34, …? (a) 258 (b) 245 (c) 251 (d) 238
  37. 37.What is the missing term in the AP 15, 20, 25, ?, 35? (a) 35 (b) 30 (c) 31 (d) 29
  38. 38.Which term of the AP 20, 26, 32, 38, … is 176? (a) 28th (b) 26th (c) 27th (d) 29th
  39. 39.What is the missing term in the AP 7, 9, ?, 13, 15? (a) 12 (b) 13 (c) 11 (d) 10
  40. 40.Which term of the AP 19, 22, 25, 28, … is 109? (a) 32nd (b) 30th (c) 31st (d) 33rd

Answer key

  1. 225
  2. 296
  3. 23
  4. 33rd
  5. 1770
  6. 234
  7. 169
  8. 1128
  9. 144
  10. 2628
  11. 19
  12. 14
  13. 196
  14. 11th
  15. 159
  16. 35th
  17. 43
  18. 34
  19. 10
  20. 132
  21. 13th
  22. 275
  23. 184
  24. 70
  25. 252
  26. 703
  27. 196
  28. 48
  29. 33
  30. 243
  31. 234
  32. 8th
  33. 80
  34. 2701
  35. 59
  36. 251
  37. 30
  38. 27th
  39. 11
  40. 31st

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