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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 706 · 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 29th term of the AP 12, 16, 20, 24, …? (a) 116 (b) 128 (c) 124 (d) 112
  2. 2.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 361 (c) 37 (d) 380
  3. 3.What is the 34th term of the AP 18, 25, 32, 39, …? (a) 238 (b) 249 (c) 231 (d) 256
  4. 4.Which term of the AP 19, 24, 29, 34, … is 199? (a) 39th (b) 36th (c) 37th (d) 38th
  5. 5.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 352 (b) 704 (c) 385 (d) 62
  6. 6.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 484 (d) 253
  7. 7.What is the sum of all the whole numbers from 1 to 13? (a) 92 (b) 78 (c) 91 (d) 182
  8. 8.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 25 (d) 9
  9. 9.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 306 (b) 324 (c) 612 (d) 42
  10. 10.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 342 (b) 189 (c) 35 (d) 171
  11. 11.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 1152 (c) 2352 (d) 1176
  12. 12.What is the missing term in the AP 17, ?, 25, 29, 33? (a) 21 (b) 22 (c) 20 (d) 25
  13. 13.What is the missing term in the AP 10, 18, 26, ?, 42? (a) 34 (b) 33 (c) 42 (d) 35
  14. 14.What is the missing term in the AP 1, ?, 9, 13, 17? (a) 5 (b) 4 (c) 9 (d) 6
  15. 15.What is the missing term in the AP 1, 5, ?, 13, 17? (a) 13 (b) 10 (c) 9 (d) 8
  16. 16.What is the 12th term of the AP 2, 4, 6, 8, …? (a) 26 (b) 24 (c) 22 (d) 25
  17. 17.What is the 10th term of the AP 2, 9, 16, 23, …? (a) 65 (b) 63 (c) 70 (d) 72
  18. 18.Which term of the AP 15, 21, 27, 33, … is 141? (a) 21st (b) 23rd (c) 22nd (d) 24th
  19. 19.What is the 32nd term of the AP 9, 17, 25, 33, …? (a) 257 (b) 248 (c) 256 (d) 265
  20. 20.What is the 20th term of the AP 1, 4, 7, 10, …? (a) 57 (b) 60 (c) 58 (d) 61
  21. 21.What is the 12th term of the AP 18, 20, 22, 24, …? (a) 42 (b) 24 (c) 22 (d) 40
  22. 22.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 520 (b) 260 (c) 44 (d) 280
  23. 23.What is the 26th term of the AP 5, 14, 23, 32, …? (a) 230 (b) 225 (c) 239 (d) 234
  24. 24.What is the missing term in the AP 8, 12, 16, ?, 24? (a) 19 (b) 24 (c) 21 (d) 20
  25. 25.What is the 10th term of the AP 3, 5, 7, 9, …? (a) 20 (b) 23 (c) 18 (d) 21
  26. 26.Which term of the AP 10, 18, 26, 34, … is 250? (a) 32nd (b) 33rd (c) 31st (d) 30th
  27. 27.What is the 25th term of the AP 9, 12, 15, 18, …? (a) 81 (b) 75 (c) 84 (d) 72
  28. 28.What is the 19th term of the AP 8, 17, 26, 35, …? (a) 171 (b) 179 (c) 170 (d) 162
  29. 29.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 250 (b) 500 (c) 270 (d) 43
  30. 30.What is the 33rd term of the AP 19, 21, 23, 25, …? (a) 64 (b) 85 (c) 66 (d) 83
  31. 31.What is the 32nd term of the AP 1, 3, 5, 7, …? (a) 64 (b) 63 (c) 65 (d) 62
  32. 32.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 49 (b) 265 (c) 290 (d) 530
  33. 33.What is the 32nd term of the AP 8, 16, 24, 32, …? (a) 257 (b) 248 (c) 256 (d) 264
  34. 34.What is the 11th term of the AP 14, 19, 24, 29, …? (a) 69 (b) 50 (c) 64 (d) 55
  35. 35.Which term of the AP 13, 16, 19, 22, … is 100? (a) 30th (b) 31st (c) 32nd (d) 29th
  36. 36.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 131 (b) 126 (c) 33 (d) 252
  37. 37.Which term of the AP 13, 19, 25, 31, … is 199? (a) 31st (b) 34th (c) 32nd (d) 33rd
  38. 38.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 132 (d) 121
  39. 39.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 138 (b) 17 (c) 144 (d) 276
  40. 40.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 39 (b) 192 (c) 344 (d) 172

Answer key

  1. 124
  2. 361
  3. 249
  4. 37th
  5. 352
  6. 484
  7. 91
  8. 25
  9. 306
  10. 171
  11. 1176
  12. 21
  13. 34
  14. 5
  15. 9
  16. 24
  17. 65
  18. 22nd
  19. 257
  20. 58
  21. 40
  22. 260
  23. 230
  24. 20
  25. 21
  26. 31st
  27. 81
  28. 170
  29. 250
  30. 83
  31. 63
  32. 265
  33. 256
  34. 64
  35. 30th
  36. 126
  37. 32nd
  38. 121
  39. 138
  40. 172

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