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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 230 · 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 15th term of the AP 19, 21, 23, 25, …? (a) 49 (b) 28 (c) 47 (d) 30
  2. 2.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 35 (d) 324
  3. 3.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 13 (b) 12 (c) 11 (d) 10
  4. 4.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 570 (b) 310 (c) 285 (d) 51
  5. 5.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2415 (c) 4970 (d) 2485
  6. 6.Which term of the AP 3, 5, 7, 9, … is 67? (a) 34th (b) 35th (c) 33rd (d) 32nd
  7. 7.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1176 (c) 1152 (d) 1128
  8. 8.What is the 21st term of the AP 9, 14, 19, 24, …? (a) 114 (b) 100 (c) 105 (d) 109
  9. 9.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 33 (b) 168 (c) 152 (d) 304
  10. 10.Which term of the AP 10, 19, 28, 37, … is 226? (a) 27th (b) 24th (c) 25th (d) 26th
  11. 11.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3570 (c) 3656 (d) 3655
  12. 12.Which term of the AP 6, 9, 12, 15, … is 108? (a) 35th (b) 37th (c) 36th (d) 34th
  13. 13.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 183 (b) 360 (c) 180 (d) 32
  14. 14.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 15 (b) 14 (c) 16 (d) 22
  15. 15.What is the 30th term of the AP 5, 13, 21, 29, …? (a) 245 (b) 232 (c) 237 (d) 240
  16. 16.What is the 11th term of the AP 4, 12, 20, 28, …? (a) 84 (b) 88 (c) 92 (d) 80
  17. 17.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 150 (b) 23 (c) 85 (d) 75
  18. 18.Which term of the AP 11, 13, 15, 17, … is 31? (a) 13th (b) 12th (c) 10th (d) 11th
  19. 19.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 15 (c) 72 (d) 36
  20. 20.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 48 (b) 90 (c) 10 (d) 45
  21. 21.What is the missing term in the AP 5, ?, 19, 26, 33? (a) 11 (b) 19 (c) 12 (d) 13
  22. 22.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 15 (d) 25
  23. 23.What is the 16th term of the AP 6, 13, 20, 27, …? (a) 112 (b) 111 (c) 105 (d) 118
  24. 24.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 144 (d) 23
  25. 25.What is the 11th term of the AP 16, 23, 30, 37, …? (a) 70 (b) 77 (c) 93 (d) 86
  26. 26.What is the 15th term of the AP 17, 19, 21, 23, …? (a) 28 (b) 30 (c) 45 (d) 47
  27. 27.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1378 (c) 1326 (d) 1352
  28. 28.Which term of the AP 15, 24, 33, 42, … is 204? (a) 23rd (b) 24th (c) 22nd (d) 21st
  29. 29.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 176 (b) 330 (c) 25 (d) 165
  30. 30.What is the sum of the first 12 terms of the AP 5, 8, 11, …? (a) 38 (b) 258 (c) 516 (d) 276
  31. 31.Which term of the AP 16, 21, 26, 31, … is 151? (a) 27th (b) 30th (c) 29th (d) 28th
  32. 32.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 9 (b) 8 (c) 10 (d) 7
  33. 33.What is the missing term in the AP 11, 19, 27, ?, 43? (a) 34 (b) 35 (c) 36 (d) 43
  34. 34.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 216 (b) 432 (c) 228 (d) 29
  35. 35.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 28 (b) 136 (c) 266 (d) 133
  36. 36.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 150 (b) 37 (c) 132 (d) 264
  37. 37.What is the 31st term of the AP 13, 21, 29, 37, …? (a) 248 (b) 253 (c) 261 (d) 240
  38. 38.What is the 13th term of the AP 13, 21, 29, 37, …? (a) 117 (b) 96 (c) 109 (d) 104
  39. 39.What is the 15th term of the AP 2, 11, 20, 29, …? (a) 128 (b) 126 (c) 135 (d) 137
  40. 40.What is the 40th term of the AP 16, 24, 32, 40, …? (a) 336 (b) 328 (c) 312 (d) 320

Answer key

  1. 47
  2. 324
  3. 11
  4. 285
  5. 2485
  6. 33rd
  7. 1176
  8. 109
  9. 152
  10. 25th
  11. 3655
  12. 35th
  13. 180
  14. 15
  15. 237
  16. 84
  17. 75
  18. 11th
  19. 64
  20. 45
  21. 12
  22. 25
  23. 111
  24. 144
  25. 86
  26. 45
  27. 1378
  28. 22nd
  29. 165
  30. 258
  31. 28th
  32. 8
  33. 35
  34. 216
  35. 133
  36. 132
  37. 253
  38. 109
  39. 128
  40. 328

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