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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 362 · 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 11 terms of the AP 8, 12, 16, …? (a) 330 (b) 308 (c) 48 (d) 616
  2. 2.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 216 (b) 384 (c) 45 (d) 192
  3. 3.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 26 (b) 18 (c) 19 (d) 20
  4. 4.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3916 (c) 7832 (d) 3872
  5. 5.What is the 14th term of the AP 15, 22, 29, 36, …? (a) 98 (b) 113 (c) 106 (d) 91
  6. 6.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 19 (d) 55
  7. 7.What is the missing term in the AP 4, 9, 14, ?, 24? (a) 19 (b) 18 (c) 24 (d) 20
  8. 8.Which term of the AP 13, 22, 31, 40, … is 301? (a) 34th (b) 33rd (c) 35th (d) 32nd
  9. 9.What is the 16th term of the AP 17, 20, 23, 26, …? (a) 45 (b) 48 (c) 65 (d) 62
  10. 10.What is the 17th term of the AP 2, 10, 18, 26, …? (a) 138 (b) 130 (c) 128 (d) 136
  11. 11.What is the sum of the first 9 terms of the AP 5, 8, 11, …? (a) 153 (b) 306 (c) 29 (d) 156
  12. 12.What is the 33rd term of the AP 20, 24, 28, 32, …? (a) 132 (b) 152 (c) 128 (d) 148
  13. 13.What is the sum of all the whole numbers from 1 to 39? (a) 781 (b) 741 (c) 1560 (d) 780
  14. 14.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 136 (b) 120 (c) 240 (d) 29
  15. 15.What is the 38th term of the AP 2, 9, 16, 23, …? (a) 266 (b) 268 (c) 259 (d) 261
  16. 16.What is the missing term in the AP 12, ?, 28, 36, 44? (a) 28 (b) 20 (c) 21 (d) 19
  17. 17.Which term of the AP 18, 23, 28, 33, … is 188? (a) 34th (b) 35th (c) 36th (d) 37th
  18. 18.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 2279 (c) 2211 (d) 4556
  19. 19.What is the missing term in the AP 19, ?, 31, 37, 43? (a) 24 (b) 25 (c) 31 (d) 26
  20. 20.What is the 17th term of the AP 10, 16, 22, 28, …? (a) 112 (b) 102 (c) 106 (d) 96
  21. 21.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 27 (b) 129 (c) 126 (d) 252
  22. 22.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 210 (d) 105
  23. 23.What is the 20th term of the AP 3, 12, 21, 30, …? (a) 174 (b) 180 (c) 183 (d) 171
  24. 24.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 31 (d) 256
  25. 25.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 171 (c) 190 (d) 380
  26. 26.What is the 40th term of the AP 3, 7, 11, 15, …? (a) 163 (b) 160 (c) 156 (d) 159
  27. 27.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 72 (d) 15
  28. 28.What is the 24th term of the AP 6, 15, 24, 33, …? (a) 216 (b) 213 (c) 207 (d) 222
  29. 29.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 1226 (c) 2450 (d) 1176
  30. 30.Which term of the AP 10, 13, 16, 19, … is 52? (a) 17th (b) 14th (c) 16th (d) 15th
  31. 31.What is the missing term in the AP 11, ?, 25, 32, 39? (a) 18 (b) 19 (c) 25 (d) 17
  32. 32.What is the 20th term of the AP 5, 8, 11, 14, …? (a) 57 (b) 60 (c) 62 (d) 65
  33. 33.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 25 (b) 23 (c) 24 (d) 28
  34. 34.Which term of the AP 12, 21, 30, 39, … is 75? (a) 10th (b) 9th (c) 7th (d) 8th
  35. 35.What is the 14th term of the AP 13, 19, 25, 31, …? (a) 97 (b) 78 (c) 84 (d) 91
  36. 36.What is the 36th term of the AP 5, 7, 9, 11, …? (a) 75 (b) 72 (c) 77 (d) 70
  37. 37.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 402 (b) 432 (c) 804 (d) 61
  38. 38.What is the 26th term of the AP 4, 7, 10, 13, …? (a) 82 (b) 75 (c) 78 (d) 79
  39. 39.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 230 (b) 430 (c) 215 (d) 35
  40. 40.What is the missing term in the AP 15, 21, ?, 33, 39? (a) 27 (b) 28 (c) 26 (d) 33

Answer key

  1. 308
  2. 192
  3. 19
  4. 3916
  5. 106
  6. 100
  7. 19
  8. 33rd
  9. 62
  10. 130
  11. 153
  12. 148
  13. 780
  14. 120
  15. 261
  16. 20
  17. 35th
  18. 2278
  19. 25
  20. 106
  21. 126
  22. 196
  23. 174
  24. 256
  25. 190
  26. 159
  27. 64
  28. 213
  29. 1225
  30. 15th
  31. 18
  32. 62
  33. 24
  34. 8th
  35. 91
  36. 75
  37. 402
  38. 79
  39. 215
  40. 27

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