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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 512 · 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 7 terms of the AP 3, 6, 9, …? (a) 84 (b) 87 (c) 21 (d) 168
  2. 2.What is the 30th term of the AP 12, 15, 18, 21, …? (a) 90 (b) 99 (c) 102 (d) 87
  3. 3.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 270 (b) 144 (c) 23 (d) 135
  4. 4.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 20 (b) 23 (c) 18 (d) 19
  5. 5.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 53 (b) 100 (c) 50 (d) 16
  6. 6.What is the 27th term of the AP 4, 12, 20, 28, …? (a) 212 (b) 216 (c) 220 (d) 208
  7. 7.What is the sum of all the whole numbers from 1 to 19? (a) 380 (b) 190 (c) 171 (d) 191
  8. 8.What is the 28th term of the AP 4, 12, 20, 28, …? (a) 216 (b) 224 (c) 220 (d) 228
  9. 9.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 11 (b) 36 (c) 72 (d) 42
  10. 10.What is the sum of all the whole numbers from 1 to 85? (a) 3655 (b) 3656 (c) 3570 (d) 7310
  11. 11.Which term of the AP 6, 9, 12, 15, … is 123? (a) 39th (b) 42nd (c) 40th (d) 41st
  12. 12.What is the 34th term of the AP 4, 10, 16, 22, …? (a) 208 (b) 198 (c) 202 (d) 204
  13. 13.What is the 15th term of the AP 4, 7, 10, 13, …? (a) 42 (b) 49 (c) 45 (d) 46
  14. 14.Which term of the AP 14, 22, 30, 38, … is 198? (a) 24th (b) 23rd (c) 25th (d) 26th
  15. 15.Which term of the AP 5, 12, 19, 26, … is 138? (a) 20th (b) 19th (c) 22nd (d) 21st
  16. 16.Which term of the AP 8, 10, 12, 14, … is 26? (a) 11th (b) 10th (c) 9th (d) 13th
  17. 17.What is the 26th term of the AP 18, 23, 28, 33, …? (a) 130 (b) 148 (c) 143 (d) 125
  18. 18.What is the 33rd term of the AP 5, 10, 15, 20, …? (a) 170 (b) 166 (c) 165 (d) 160
  19. 19.What is the 22nd term of the AP 4, 6, 8, 10, …? (a) 42 (b) 46 (c) 44 (d) 48
  20. 20.What is the missing term in the AP 12, ?, 16, 18, 20? (a) 13 (b) 14 (c) 16 (d) 15
  21. 21.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4754 (c) 4753 (d) 4656
  22. 22.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 88 (b) 44 (c) 9 (d) 48
  23. 23.What is the missing term in the AP 12, 19, ?, 33, 40? (a) 27 (b) 26 (c) 25 (d) 33
  24. 24.What is the 12th term of the AP 2, 4, 6, 8, …? (a) 25 (b) 26 (c) 22 (d) 24
  25. 25.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 88 (b) 13 (c) 176 (d) 89
  26. 26.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 164 (b) 38 (c) 328 (d) 184
  27. 27.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 484 (d) 253
  28. 28.What is the sum of the first 11 terms of the AP 10, 15, 20, …? (a) 60 (b) 385 (c) 770 (d) 390
  29. 29.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 27 (d) 196
  30. 30.Which term of the AP 13, 16, 19, 22, … is 73? (a) 20th (b) 21st (c) 23rd (d) 22nd
  31. 31.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 20 (b) 21 (c) 18 (d) 19
  32. 32.What is the 26th term of the AP 16, 18, 20, 22, …? (a) 68 (b) 50 (c) 66 (d) 52
  33. 33.What is the 28th term of the AP 4, 8, 12, 16, …? (a) 116 (b) 113 (c) 108 (d) 112
  34. 34.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 36 (b) 148 (c) 168 (d) 296
  35. 35.What is the 30th term of the AP 17, 21, 25, 29, …? (a) 133 (b) 120 (c) 137 (d) 116
  36. 36.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 361 (d) 380
  37. 37.What is the sum of all the whole numbers from 1 to 55? (a) 3080 (b) 1485 (c) 1541 (d) 1540
  38. 38.What is the missing term in the AP 6, 9, ?, 15, 18? (a) 13 (b) 11 (c) 12 (d) 15
  39. 39.What is the 38th term of the AP 20, 29, 38, 47, …? (a) 333 (b) 362 (c) 342 (d) 353
  40. 40.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 60 (b) 420 (c) 390 (d) 780

Answer key

  1. 84
  2. 99
  3. 135
  4. 19
  5. 50
  6. 212
  7. 190
  8. 220
  9. 36
  10. 3655
  11. 40th
  12. 202
  13. 46
  14. 24th
  15. 20th
  16. 10th
  17. 143
  18. 165
  19. 46
  20. 14
  21. 4753
  22. 44
  23. 26
  24. 24
  25. 88
  26. 164
  27. 484
  28. 385
  29. 196
  30. 21st
  31. 19
  32. 66
  33. 112
  34. 148
  35. 133
  36. 361
  37. 1540
  38. 12
  39. 353
  40. 390

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