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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 227 · 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.Which term of the AP 6, 15, 24, 33, … is 150? (a) 16th (b) 18th (c) 17th (d) 19th
  2. 2.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 162 (b) 30 (c) 324 (d) 165
  3. 3.Which term of the AP 15, 20, 25, 30, … is 110? (a) 20th (b) 22nd (c) 21st (d) 19th
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 210 (c) 105 (d) 196
  5. 5.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 286 (b) 308 (c) 46 (d) 572
  6. 6.What is the 24th term of the AP 5, 11, 17, 23, …? (a) 144 (b) 149 (c) 143 (d) 138
  7. 7.What is the missing term in the AP 2, 5, ?, 11, 14? (a) 7 (b) 11 (c) 9 (d) 8
  8. 8.Which term of the AP 8, 10, 12, 14, … is 32? (a) 13th (b) 16th (c) 14th (d) 12th
  9. 9.What is the 32nd term of the AP 3, 6, 9, 12, …? (a) 97 (b) 93 (c) 99 (d) 96
  10. 10.What is the 12th term of the AP 4, 11, 18, 25, …? (a) 88 (b) 84 (c) 81 (d) 77
  11. 11.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3486 (c) 3528 (d) 3570
  12. 12.What is the 30th term of the AP 9, 17, 25, 33, …? (a) 240 (b) 249 (c) 232 (d) 241
  13. 13.What is the 30th term of the AP 7, 11, 15, 19, …? (a) 116 (b) 123 (c) 127 (d) 120
  14. 14.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 81 (d) 17
  15. 15.Which term of the AP 16, 25, 34, 43, … is 367? (a) 39th (b) 40th (c) 42nd (d) 41st
  16. 16.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 506 (c) 43 (d) 484
  17. 17.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 127 (b) 252 (c) 126 (d) 18
  18. 18.What is the 27th term of the AP 3, 12, 21, 30, …? (a) 246 (b) 237 (c) 234 (d) 243
  19. 19.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 59 (c) 930 (d) 465
  20. 20.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4656 (c) 4753 (d) 4754
  21. 21.Which term of the AP 7, 14, 21, 28, … is 140? (a) 19th (b) 20th (c) 21st (d) 22nd
  22. 22.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 870 (d) 841
  23. 23.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 342 (c) 171 (d) 153
  24. 24.Which term of the AP 4, 13, 22, 31, … is 202? (a) 22nd (b) 23rd (c) 24th (d) 25th
  25. 25.What is the missing term in the AP 11, 17, 23, ?, 35? (a) 28 (b) 35 (c) 29 (d) 30
  26. 26.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 64 (d) 72
  27. 27.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 144 (b) 78 (c) 17 (d) 72
  28. 28.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 54 (b) 630 (c) 315 (d) 340
  29. 29.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 47 (d) 576
  30. 30.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 15 (b) 13 (c) 12 (d) 14
  31. 31.What is the 32nd term of the AP 1, 10, 19, 28, …? (a) 279 (b) 280 (c) 288 (d) 289
  32. 32.What is the 17th term of the AP 20, 23, 26, 29, …? (a) 71 (b) 48 (c) 68 (d) 51
  33. 33.What is the 24th term of the AP 18, 27, 36, 45, …? (a) 225 (b) 207 (c) 234 (d) 216
  34. 34.What is the missing term in the AP 13, 20, ?, 34, 41? (a) 28 (b) 26 (c) 34 (d) 27
  35. 35.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 121 (d) 132
  36. 36.What is the 17th term of the AP 16, 25, 34, 43, …? (a) 160 (b) 153 (c) 144 (d) 169
  37. 37.What is the missing term in the AP 16, 22, 28, ?, 40? (a) 35 (b) 40 (c) 33 (d) 34
  38. 38.What is the 38th term of the AP 9, 14, 19, 24, …? (a) 199 (b) 185 (c) 190 (d) 194
  39. 39.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 1176 (c) 2352 (d) 1152
  40. 40.What is the missing term in the AP 11, ?, 29, 38, 47? (a) 19 (b) 21 (c) 29 (d) 20

Answer key

  1. 17th
  2. 162
  3. 20th
  4. 196
  5. 286
  6. 143
  7. 8
  8. 13th
  9. 96
  10. 81
  11. 3570
  12. 241
  13. 123
  14. 81
  15. 40th
  16. 484
  17. 126
  18. 237
  19. 900
  20. 4753
  21. 20th
  22. 841
  23. 171
  24. 23rd
  25. 29
  26. 64
  27. 72
  28. 315
  29. 576
  30. 13
  31. 280
  32. 68
  33. 225
  34. 27
  35. 121
  36. 160
  37. 34
  38. 194
  39. 1176
  40. 20

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