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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 708 · 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 20th term of the AP 17, 22, 27, 32, …? (a) 117 (b) 112 (c) 95 (d) 100
  2. 2.What is the 24th term of the AP 13, 22, 31, 40, …? (a) 229 (b) 220 (c) 216 (d) 207
  3. 3.What is the missing term in the AP 20, ?, 32, 38, 44? (a) 25 (b) 26 (c) 27 (d) 32
  4. 4.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 256 (b) 144 (c) 128 (d) 30
  5. 5.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 189 (b) 42 (c) 168 (d) 336
  6. 6.Which term of the AP 12, 19, 26, 33, … is 75? (a) 10th (b) 12th (c) 9th (d) 11th
  7. 7.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3486 (c) 3528 (d) 3570
  8. 8.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 90 (d) 81
  9. 9.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 380 (d) 361
  10. 10.What is the missing term in the AP 14, 20, ?, 32, 38? (a) 32 (b) 27 (c) 26 (d) 25
  11. 11.What is the 18th term of the AP 9, 12, 15, 18, …? (a) 54 (b) 63 (c) 60 (d) 51
  12. 12.Which term of the AP 2, 5, 8, 11, … is 119? (a) 42nd (b) 41st (c) 39th (d) 40th
  13. 13.What is the missing term in the AP 17, ?, 33, 41, 49? (a) 25 (b) 26 (c) 33 (d) 24
  14. 14.What is the 33rd term of the AP 11, 13, 15, 17, …? (a) 77 (b) 64 (c) 66 (d) 75
  15. 15.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 289 (c) 33 (d) 306
  16. 16.What is the 10th term of the AP 8, 11, 14, 17, …? (a) 38 (b) 30 (c) 35 (d) 27
  17. 17.What is the missing term in the AP 12, 17, 22, ?, 32? (a) 26 (b) 32 (c) 27 (d) 28
  18. 18.What is the 11th term of the AP 17, 25, 33, 41, …? (a) 88 (b) 97 (c) 105 (d) 80
  19. 19.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 465 (c) 930 (d) 435
  20. 20.What is the sum of the first 7 terms of the AP 8, 12, 16, …? (a) 140 (b) 154 (c) 280 (d) 32
  21. 21.What is the missing term in the AP 19, 27, 35, ?, 51? (a) 44 (b) 42 (c) 51 (d) 43
  22. 22.Which term of the AP 13, 21, 29, 37, … is 157? (a) 21st (b) 18th (c) 19th (d) 20th
  23. 23.What is the 27th term of the AP 10, 15, 20, 25, …? (a) 130 (b) 145 (c) 135 (d) 140
  24. 24.What is the 18th term of the AP 10, 14, 18, 22, …? (a) 82 (b) 78 (c) 72 (d) 68
  25. 25.What is the 18th term of the AP 17, 24, 31, 38, …? (a) 119 (b) 126 (c) 136 (d) 143
  26. 26.What is the 37th term of the AP 18, 25, 32, 39, …? (a) 270 (b) 277 (c) 259 (d) 252
  27. 27.What is the 12th term of the AP 5, 9, 13, 17, …? (a) 44 (b) 49 (c) 48 (d) 53
  28. 28.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 378 (c) 351 (d) 756
  29. 29.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
  30. 30.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 3192 (c) 1540 (d) 1596
  31. 31.Which term of the AP 3, 7, 11, 15, … is 47? (a) 11th (b) 12th (c) 13th (d) 14th
  32. 32.What is the 38th term of the AP 2, 9, 16, 23, …? (a) 266 (b) 268 (c) 261 (d) 259
  33. 33.Which term of the AP 20, 24, 28, 32, … is 56? (a) 9th (b) 11th (c) 10th (d) 14th
  34. 34.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 2556 (c) 5112 (d) 2557
  35. 35.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 72 (b) 42 (c) 11 (d) 36
  36. 36.What is the 14th term of the AP 16, 22, 28, 34, …? (a) 94 (b) 84 (c) 100 (d) 78
  37. 37.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 580 (b) 290 (c) 56 (d) 320
  38. 38.What is the missing term in the AP 16, ?, 20, 22, 24? (a) 19 (b) 18 (c) 17 (d) 20
  39. 39.What is the sum of all the whole numbers from 1 to 54? (a) 1485 (b) 2970 (c) 1458 (d) 1431
  40. 40.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 486 (b) 248 (c) 243 (d) 47

Answer key

  1. 112
  2. 220
  3. 26
  4. 128
  5. 168
  6. 10th
  7. 3570
  8. 81
  9. 361
  10. 26
  11. 60
  12. 40th
  13. 25
  14. 75
  15. 289
  16. 35
  17. 27
  18. 97
  19. 465
  20. 140
  21. 43
  22. 19th
  23. 140
  24. 78
  25. 136
  26. 270
  27. 49
  28. 378
  29. 100
  30. 1596
  31. 12th
  32. 261
  33. 10th
  34. 2556
  35. 36
  36. 94
  37. 290
  38. 18
  39. 1485
  40. 243

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