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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 759 · 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 10 terms of the AP 10, 13, 16, …? (a) 235 (b) 250 (c) 470 (d) 37
  2. 2.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 19 (b) 324 (c) 162 (d) 168
  3. 3.What is the sum of the first 12 terms of the AP 10, 16, 22, …? (a) 1032 (b) 76 (c) 552 (d) 516
  4. 4.What is the 12th term of the AP 20, 24, 28, 32, …? (a) 44 (b) 68 (c) 64 (d) 48
  5. 5.Which term of the AP 19, 22, 25, 28, … is 100? (a) 27th (b) 30th (c) 29th (d) 28th
  6. 6.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 29 (b) 100 (c) 170 (d) 85
  7. 7.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 288 (b) 46 (c) 312 (d) 576
  8. 8.Which term of the AP 20, 28, 36, 44, … is 244? (a) 28th (b) 30th (c) 31st (d) 29th
  9. 9.What is the 18th term of the AP 4, 11, 18, 25, …? (a) 126 (b) 130 (c) 119 (d) 123
  10. 10.Which term of the AP 13, 17, 21, 25, … is 49? (a) 11th (b) 12th (c) 9th (d) 10th
  11. 11.What is the 33rd term of the AP 4, 7, 10, 13, …? (a) 99 (b) 103 (c) 100 (d) 96
  12. 12.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 253 (c) 484 (d) 43
  13. 13.What is the missing term in the AP 8, 12, ?, 20, 24? (a) 16 (b) 15 (c) 20 (d) 17
  14. 14.What is the sum of the first 8 terms of the AP 4, 7, 10, …? (a) 232 (b) 128 (c) 25 (d) 116
  15. 15.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 2080 (c) 2048 (d) 4160
  16. 16.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 380 (d) 37
  17. 17.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 50 (b) 336 (c) 360 (d) 672
  18. 18.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 81 (d) 45
  19. 19.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 210 (b) 110 (c) 105 (d) 15
  20. 20.What is the 10th term of the AP 14, 16, 18, 20, …? (a) 32 (b) 20 (c) 34 (d) 18
  21. 21.What is the 15th term of the AP 1, 9, 17, 25, …? (a) 121 (b) 120 (c) 112 (d) 113
  22. 22.What is the 40th term of the AP 19, 25, 31, 37, …? (a) 234 (b) 253 (c) 259 (d) 240
  23. 23.What is the 10th term of the AP 6, 11, 16, 21, …? (a) 50 (b) 51 (c) 45 (d) 56
  24. 24.What is the missing term in the AP 9, 13, ?, 21, 25? (a) 18 (b) 16 (c) 17 (d) 21
  25. 25.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 108 (b) 186 (c) 28 (d) 93
  26. 26.What is the missing term in the AP 11, ?, 29, 38, 47? (a) 19 (b) 29 (c) 21 (d) 20
  27. 27.What is the 13th term of the AP 8, 16, 24, 32, …? (a) 104 (b) 105 (c) 96 (d) 112
  28. 28.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 9 (b) 48 (c) 88 (d) 44
  29. 29.What is the 19th term of the AP 14, 19, 24, 29, …? (a) 90 (b) 95 (c) 109 (d) 104
  30. 30.What is the 14th term of the AP 12, 14, 16, 18, …? (a) 40 (b) 28 (c) 26 (d) 38
  31. 31.What is the 33rd term of the AP 20, 24, 28, 32, …? (a) 132 (b) 148 (c) 128 (d) 152
  32. 32.What is the 17th term of the AP 13, 17, 21, 25, …? (a) 77 (b) 64 (c) 68 (d) 81
  33. 33.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 22 (b) 80 (c) 140 (d) 70
  34. 34.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 154 (b) 80 (c) 20 (d) 77
  35. 35.What is the 32nd term of the AP 11, 13, 15, 17, …? (a) 73 (b) 75 (c) 64 (d) 62
  36. 36.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 374 (b) 379 (c) 748 (d) 59
  37. 37.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 25 (c) 15 (d) 9
  38. 38.What is the missing term in the AP 14, 18, ?, 26, 30? (a) 23 (b) 22 (c) 21 (d) 26
  39. 39.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 1596 (c) 3192 (d) 1568
  40. 40.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 1260 (c) 631 (d) 595

Answer key

  1. 235
  2. 162
  3. 516
  4. 64
  5. 28th
  6. 85
  7. 288
  8. 29th
  9. 123
  10. 10th
  11. 100
  12. 484
  13. 16
  14. 116
  15. 2080
  16. 361
  17. 336
  18. 81
  19. 105
  20. 32
  21. 113
  22. 253
  23. 51
  24. 17
  25. 93
  26. 20
  27. 104
  28. 44
  29. 104
  30. 38
  31. 148
  32. 77
  33. 70
  34. 77
  35. 73
  36. 374
  37. 25
  38. 22
  39. 1596
  40. 630

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