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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 569 · 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 all the whole numbers from 1 to 93? (a) 4372 (b) 4278 (c) 4371 (d) 8742
  2. 2.What is the 14th term of the AP 17, 23, 29, 35, …? (a) 84 (b) 78 (c) 95 (d) 101
  3. 3.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 88 (b) 168 (c) 14 (d) 84
  4. 4.What is the sum of the first 8 terms of the AP 6, 11, 16, …? (a) 41 (b) 188 (c) 376 (d) 208
  5. 5.Which term of the AP 13, 16, 19, 22, … is 82? (a) 26th (b) 25th (c) 23rd (d) 24th
  6. 6.What is the missing term in the AP 17, ?, 31, 38, 45? (a) 23 (b) 25 (c) 24 (d) 31
  7. 7.What is the 28th term of the AP 10, 12, 14, 16, …? (a) 66 (b) 54 (c) 56 (d) 64
  8. 8.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 150 (b) 75 (c) 85 (d) 23
  9. 9.Which term of the AP 8, 16, 24, 32, … is 184? (a) 24th (b) 22nd (c) 23rd (d) 25th
  10. 10.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 374 (b) 682 (c) 61 (d) 341
  11. 11.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 182 (d) 169
  12. 12.Which term of the AP 7, 14, 21, 28, … is 210? (a) 31st (b) 30th (c) 29th (d) 32nd
  13. 13.What is the sum of all the whole numbers from 1 to 43? (a) 947 (b) 903 (c) 946 (d) 1892
  14. 14.Which term of the AP 19, 26, 33, 40, … is 89? (a) 12th (b) 10th (c) 13th (d) 11th
  15. 15.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 64 (d) 36
  16. 16.What is the 39th term of the AP 14, 21, 28, 35, …? (a) 273 (b) 280 (c) 266 (d) 287
  17. 17.What is the 39th term of the AP 5, 14, 23, 32, …? (a) 342 (b) 351 (c) 356 (d) 347
  18. 18.What is the 13th term of the AP 9, 11, 13, 15, …? (a) 24 (b) 26 (c) 33 (d) 35
  19. 19.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 900 (c) 465 (d) 59
  20. 20.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 28 (b) 120 (c) 216 (d) 108
  21. 21.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 5700 (c) 2851 (d) 2850
  22. 22.What is the 39th term of the AP 9, 14, 19, 24, …? (a) 195 (b) 199 (c) 204 (d) 190
  23. 23.Which term of the AP 17, 26, 35, 44, … is 269? (a) 29th (b) 30th (c) 28th (d) 31st
  24. 24.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 18 (b) 13 (c) 12 (d) 11
  25. 25.What is the 37th term of the AP 5, 13, 21, 29, …? (a) 296 (b) 293 (c) 301 (d) 288
  26. 26.What is the sum of the first 8 terms of the AP 9, 14, 19, …? (a) 232 (b) 44 (c) 212 (d) 424
  27. 27.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 6 (b) 21 (c) 42 (d) 24
  28. 28.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 45 (d) 529
  29. 29.What is the 13th term of the AP 6, 8, 10, 12, …? (a) 26 (b) 30 (c) 32 (d) 24
  30. 30.What is the 27th term of the AP 20, 24, 28, 32, …? (a) 128 (b) 124 (c) 108 (d) 104
  31. 31.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 95 (b) 80 (c) 160 (d) 28
  32. 32.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 85 (b) 95 (c) 25 (d) 170
  33. 33.What is the sum of the first 8 terms of the AP 4, 10, 16, …? (a) 46 (b) 200 (c) 224 (d) 400
  34. 34.What is the 39th term of the AP 12, 17, 22, 27, …? (a) 202 (b) 207 (c) 195 (d) 190
  35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 100 (d) 110
  36. 36.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 9 (b) 10 (c) 11 (d) 14
  37. 37.What is the 30th term of the AP 11, 18, 25, 32, …? (a) 203 (b) 214 (c) 221 (d) 210
  38. 38.What is the 24th term of the AP 13, 20, 27, 34, …? (a) 174 (b) 161 (c) 181 (d) 168
  39. 39.What is the 17th term of the AP 18, 21, 24, 27, …? (a) 48 (b) 66 (c) 51 (d) 69
  40. 40.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 190 (b) 29 (c) 95 (d) 100

Answer key

  1. 4371
  2. 95
  3. 84
  4. 188
  5. 24th
  6. 24
  7. 64
  8. 75
  9. 23rd
  10. 341
  11. 169
  12. 30th
  13. 946
  14. 11th
  15. 64
  16. 280
  17. 347
  18. 33
  19. 900
  20. 108
  21. 2850
  22. 199
  23. 29th
  24. 12
  25. 293
  26. 212
  27. 21
  28. 529
  29. 30
  30. 124
  31. 80
  32. 85
  33. 200
  34. 202
  35. 100
  36. 10
  37. 214
  38. 174
  39. 66
  40. 95

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