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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 270 · 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 8 terms of the AP 6, 7, 8, …? (a) 80 (b) 152 (c) 76 (d) 13
  2. 2.What is the 27th term of the AP 17, 24, 31, 38, …? (a) 199 (b) 189 (c) 182 (d) 206
  3. 3.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 100 (d) 19
  4. 4.What is the 20th term of the AP 20, 29, 38, 47, …? (a) 171 (b) 180 (c) 191 (d) 200
  5. 5.What is the sum of all the whole numbers from 1 to 60? (a) 1770 (b) 3660 (c) 1800 (d) 1830
  6. 6.What is the missing term in the AP 17, ?, 31, 38, 45? (a) 25 (b) 31 (c) 24 (d) 23
  7. 7.Which term of the AP 13, 17, 21, 25, … is 41? (a) 9th (b) 10th (c) 8th (d) 7th
  8. 8.What is the sum of all the whole numbers from 1 to 62? (a) 3906 (b) 1922 (c) 1953 (d) 1891
  9. 9.What is the missing term in the AP 5, ?, 23, 32, 41? (a) 15 (b) 23 (c) 14 (d) 13
  10. 10.What is the sum of the first 11 terms of the AP 5, 10, 15, …? (a) 660 (b) 335 (c) 330 (d) 55
  11. 11.What is the 34th term of the AP 16, 21, 26, 31, …? (a) 165 (b) 181 (c) 170 (d) 186
  12. 12.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 136 (b) 23 (c) 256 (d) 128
  13. 13.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 240 (b) 222 (c) 35 (d) 444
  14. 14.What is the 14th term of the AP 9, 18, 27, 36, …? (a) 135 (b) 127 (c) 117 (d) 126
  15. 15.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 210 (d) 196
  16. 16.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 400 (c) 39 (d) 210
  17. 17.What is the sum of all the whole numbers from 1 to 74? (a) 5550 (b) 2775 (c) 2738 (d) 2701
  18. 18.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 63 (b) 13 (c) 126 (d) 66
  19. 19.What is the 28th term of the AP 17, 26, 35, 44, …? (a) 243 (b) 260 (c) 269 (d) 252
  20. 20.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 120 (b) 32 (c) 204 (d) 102
  21. 21.What is the 25th term of the AP 7, 16, 25, 34, …? (a) 223 (b) 225 (c) 216 (d) 232
  22. 22.Which term of the AP 1, 8, 15, 22, … is 99? (a) 15th (b) 14th (c) 17th (d) 16th
  23. 23.What is the 22nd term of the AP 20, 29, 38, 47, …? (a) 198 (b) 218 (c) 209 (d) 189
  24. 24.What is the sum of all the whole numbers from 1 to 24? (a) 300 (b) 600 (c) 288 (d) 276
  25. 25.What is the missing term in the AP 9, 13, 17, ?, 25? (a) 21 (b) 20 (c) 25 (d) 22
  26. 26.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 37 (b) 176 (c) 156 (d) 312
  27. 27.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 156 (c) 144 (d) 78
  28. 28.What is the missing term in the AP 13, 21, ?, 37, 45? (a) 28 (b) 37 (c) 29 (d) 30
  29. 29.What is the sum of all the whole numbers from 1 to 22? (a) 253 (b) 242 (c) 506 (d) 231
  30. 30.What is the 12th term of the AP 8, 13, 18, 23, …? (a) 68 (b) 60 (c) 55 (d) 63
  31. 31.What is the 37th term of the AP 4, 8, 12, 16, …? (a) 144 (b) 148 (c) 152 (d) 149
  32. 32.What is the missing term in the AP 3, 12, 21, ?, 39? (a) 31 (b) 39 (c) 30 (d) 29
  33. 33.What is the missing term in the AP 11, 18, 25, ?, 39? (a) 39 (b) 31 (c) 33 (d) 32
  34. 34.Which term of the AP 5, 13, 21, 29, … is 101? (a) 14th (b) 12th (c) 13th (d) 15th
  35. 35.What is the 26th term of the AP 8, 14, 20, 26, …? (a) 158 (b) 164 (c) 156 (d) 150
  36. 36.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 561 (c) 528 (d) 562
  37. 37.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 784 (d) 406
  38. 38.What is the missing term in the AP 15, 23, 31, ?, 47? (a) 39 (b) 47 (c) 40 (d) 38
  39. 39.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 400 (b) 64 (c) 370 (d) 740
  40. 40.What is the sum of all the whole numbers from 1 to 95? (a) 4560 (b) 4465 (c) 4561 (d) 9120

Answer key

  1. 76
  2. 199
  3. 100
  4. 191
  5. 1830
  6. 24
  7. 8th
  8. 1953
  9. 14
  10. 330
  11. 181
  12. 128
  13. 222
  14. 126
  15. 196
  16. 400
  17. 2775
  18. 63
  19. 260
  20. 102
  21. 223
  22. 15th
  23. 209
  24. 300
  25. 21
  26. 156
  27. 144
  28. 29
  29. 253
  30. 63
  31. 148
  32. 30
  33. 32
  34. 13th
  35. 158
  36. 561
  37. 784
  38. 39
  39. 370
  40. 4560

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