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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 196 · 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 18th term of the AP 14, 22, 30, 38, …? (a) 158 (b) 136 (c) 144 (d) 150
  2. 2.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 132 (c) 55 (d) 67
  3. 3.What is the 11th term of the AP 7, 15, 23, 31, …? (a) 87 (b) 95 (c) 88 (d) 80
  4. 4.What is the 18th term of the AP 16, 19, 22, 25, …? (a) 54 (b) 51 (c) 67 (d) 70
  5. 5.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 1152 (c) 2352 (d) 1176
  6. 6.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 30 (d) 25
  7. 7.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 216 (b) 396 (c) 38 (d) 198
  8. 8.Which term of the AP 16, 18, 20, 22, … is 40? (a) 12th (b) 14th (c) 13th (d) 20th
  9. 9.Which term of the AP 20, 28, 36, 44, … is 244? (a) 31st (b) 30th (c) 29th (d) 28th
  10. 10.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 132 (d) 21
  11. 11.Which term of the AP 16, 21, 26, 31, … is 61? (a) 12th (b) 9th (c) 10th (d) 11th
  12. 12.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 110 (c) 55 (d) 45
  13. 13.What is the 34th term of the AP 19, 28, 37, 46, …? (a) 316 (b) 325 (c) 306 (d) 297
  14. 14.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 812 (c) 378 (d) 406
  15. 15.Which term of the AP 18, 26, 34, 42, … is 74? (a) 7th (b) 9th (c) 10th (d) 8th
  16. 16.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 42 (c) 11 (d) 21
  17. 17.What is the 25th term of the AP 18, 23, 28, 33, …? (a) 138 (b) 125 (c) 143 (d) 120
  18. 18.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 47 (b) 243 (c) 486 (d) 248
  19. 19.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 67 (b) 814 (c) 407 (d) 440
  20. 20.What is the 17th term of the AP 3, 9, 15, 21, …? (a) 102 (b) 96 (c) 99 (d) 105
  21. 21.What is the 23rd term of the AP 18, 20, 22, 24, …? (a) 44 (b) 46 (c) 62 (d) 64
  22. 22.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 19 (d) 55
  23. 23.What is the missing term in the AP 8, ?, 24, 32, 40? (a) 24 (b) 15 (c) 16 (d) 17
  24. 24.What is the 16th term of the AP 13, 16, 19, 22, …? (a) 48 (b) 45 (c) 58 (d) 61
  25. 25.What is the 13th term of the AP 16, 23, 30, 37, …? (a) 100 (b) 107 (c) 84 (d) 91
  26. 26.Which term of the AP 20, 23, 26, 29, … is 107? (a) 32nd (b) 29th (c) 31st (d) 30th
  27. 27.Which term of the AP 15, 19, 23, 27, … is 83? (a) 20th (b) 19th (c) 17th (d) 18th
  28. 28.What is the 36th term of the AP 20, 25, 30, 35, …? (a) 195 (b) 175 (c) 200 (d) 180
  29. 29.What is the missing term in the AP 18, 23, 28, ?, 38? (a) 33 (b) 34 (c) 38 (d) 32
  30. 30.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 740 (b) 370 (c) 64 (d) 400
  31. 31.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 59 (c) 465 (d) 930
  32. 32.What is the 15th term of the AP 4, 13, 22, 31, …? (a) 139 (b) 126 (c) 135 (d) 130
  33. 33.What is the 33rd term of the AP 11, 15, 19, 23, …? (a) 143 (b) 139 (c) 128 (d) 132
  34. 34.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 1129 (c) 1128 (d) 2256
  35. 35.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 3528 (c) 7140 (d) 3570
  36. 36.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 3362 (c) 6806 (d) 3321
  37. 37.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 50 (b) 14 (c) 55 (d) 100
  38. 38.What is the 28th term of the AP 15, 23, 31, 39, …? (a) 231 (b) 224 (c) 239 (d) 216
  39. 39.What is the 12th term of the AP 11, 18, 25, 32, …? (a) 95 (b) 77 (c) 88 (d) 84
  40. 40.What is the 38th term of the AP 4, 12, 20, 28, …? (a) 308 (b) 304 (c) 296 (d) 300

Answer key

  1. 150
  2. 66
  3. 87
  4. 67
  5. 1176
  6. 25
  7. 198
  8. 13th
  9. 29th
  10. 121
  11. 10th
  12. 55
  13. 316
  14. 406
  15. 8th
  16. 36
  17. 138
  18. 243
  19. 407
  20. 99
  21. 62
  22. 100
  23. 16
  24. 58
  25. 100
  26. 30th
  27. 18th
  28. 195
  29. 33
  30. 370
  31. 900
  32. 130
  33. 139
  34. 1128
  35. 3570
  36. 3403
  37. 50
  38. 231
  39. 88
  40. 300

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