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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 430 · 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 40th term of the AP 10, 19, 28, 37, …? (a) 351 (b) 370 (c) 360 (d) 361
  2. 2.What is the 33rd term of the AP 14, 20, 26, 32, …? (a) 198 (b) 192 (c) 206 (d) 212
  3. 3.What is the 33rd term of the AP 19, 22, 25, 28, …? (a) 99 (b) 115 (c) 118 (d) 96
  4. 4.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 169 (d) 25
  5. 5.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 12 (b) 13 (c) 11 (d) 18
  6. 6.What is the missing term in the AP 19, 23, 27, ?, 35? (a) 35 (b) 32 (c) 30 (d) 31
  7. 7.What is the 38th term of the AP 3, 7, 11, 15, …? (a) 155 (b) 148 (c) 151 (d) 152
  8. 8.What is the 15th term of the AP 1, 10, 19, 28, …? (a) 126 (b) 136 (c) 135 (d) 127
  9. 9.Which term of the AP 9, 11, 13, 15, … is 59? (a) 28th (b) 25th (c) 27th (d) 26th
  10. 10.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 3081 (c) 6320 (d) 3160
  11. 11.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 175 (b) 180 (c) 350 (d) 40
  12. 12.Which term of the AP 16, 20, 24, 28, … is 144? (a) 36th (b) 32nd (c) 33rd (d) 34th
  13. 13.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 21 (b) 40 (c) 20 (d) 6
  14. 14.Which term of the AP 7, 11, 15, 19, … is 127? (a) 31st (b) 30th (c) 33rd (d) 32nd
  15. 15.What is the 37th term of the AP 6, 12, 18, 24, …? (a) 216 (b) 222 (c) 223 (d) 228
  16. 16.What is the 35th term of the AP 4, 12, 20, 28, …? (a) 276 (b) 280 (c) 272 (d) 284
  17. 17.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 68 (b) 451 (c) 836 (d) 418
  18. 18.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 529 (c) 276 (d) 552
  19. 19.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 2485 (c) 4970 (d) 2450
  20. 20.Which term of the AP 17, 25, 33, 41, … is 241? (a) 28th (b) 31st (c) 29th (d) 30th
  21. 21.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 740 (b) 64 (c) 400 (d) 370
  22. 22.What is the 15th term of the AP 16, 25, 34, 43, …? (a) 142 (b) 126 (c) 135 (d) 151
  23. 23.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 15 (b) 90 (c) 45 (d) 48
  24. 24.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 210 (c) 196 (d) 105
  25. 25.Which term of the AP 13, 16, 19, 22, … is 64? (a) 18th (b) 17th (c) 20th (d) 19th
  26. 26.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 16 (b) 17 (c) 15 (d) 22
  27. 27.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 484 (c) 43 (d) 253
  28. 28.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 15 (b) 19 (c) 14 (d) 16
  29. 29.What is the 40th term of the AP 14, 18, 22, 26, …? (a) 156 (b) 174 (c) 160 (d) 170
  30. 30.What is the 29th term of the AP 5, 11, 17, 23, …? (a) 168 (b) 179 (c) 174 (d) 173
  31. 31.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 351 (c) 702 (d) 325
  32. 32.What is the 18th term of the AP 19, 26, 33, 40, …? (a) 126 (b) 119 (c) 145 (d) 138
  33. 33.What is the 11th term of the AP 6, 10, 14, 18, …? (a) 46 (b) 50 (c) 40 (d) 44
  34. 34.Which term of the AP 19, 24, 29, 34, … is 204? (a) 37th (b) 38th (c) 40th (d) 39th
  35. 35.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 225 (c) 240 (d) 29
  36. 36.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 19 (d) 110
  37. 37.What is the sum of all the whole numbers from 1 to 46? (a) 1035 (b) 2162 (c) 1058 (d) 1081
  38. 38.What is the 26th term of the AP 4, 13, 22, 31, …? (a) 225 (b) 238 (c) 234 (d) 229
  39. 39.What is the sum of all the whole numbers from 1 to 30? (a) 465 (b) 930 (c) 435 (d) 450
  40. 40.Which term of the AP 3, 12, 21, 30, … is 345? (a) 40th (b) 38th (c) 39th (d) 41st

Answer key

  1. 361
  2. 206
  3. 115
  4. 169
  5. 12
  6. 31
  7. 151
  8. 127
  9. 26th
  10. 3160
  11. 175
  12. 33rd
  13. 20
  14. 31st
  15. 222
  16. 276
  17. 418
  18. 529
  19. 2485
  20. 29th
  21. 370
  22. 142
  23. 45
  24. 196
  25. 18th
  26. 16
  27. 484
  28. 15
  29. 170
  30. 173
  31. 351
  32. 138
  33. 46
  34. 38th
  35. 225
  36. 100
  37. 1081
  38. 229
  39. 465
  40. 39th

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