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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 157 · 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 6 terms of the AP 1, 5, 9, …? (a) 21 (b) 132 (c) 78 (d) 66
  2. 2.What is the 24th term of the AP 5, 8, 11, 14, …? (a) 74 (b) 77 (c) 72 (d) 69
  3. 3.Which term of the AP 4, 13, 22, 31, … is 211? (a) 23rd (b) 24th (c) 25th (d) 26th
  4. 4.What is the 37th term of the AP 12, 21, 30, 39, …? (a) 336 (b) 324 (c) 333 (d) 345
  5. 5.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 7140 (c) 3570 (d) 3486
  6. 6.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 114 (b) 66 (c) 57 (d) 17
  7. 7.What is the 31st term of the AP 12, 20, 28, 36, …? (a) 248 (b) 260 (c) 252 (d) 240
  8. 8.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 115 (b) 112 (c) 25 (d) 224
  9. 9.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 256 (b) 30 (c) 144 (d) 128
  10. 10.What is the missing term in the AP 16, 18, ?, 22, 24? (a) 22 (b) 19 (c) 20 (d) 21
  11. 11.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
  12. 12.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 9 (c) 30 (d) 15
  13. 13.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 40 (b) 21 (c) 6 (d) 20
  14. 14.What is the sum of all the whole numbers from 1 to 43? (a) 947 (b) 1892 (c) 946 (d) 903
  15. 15.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 190 (d) 37
  16. 16.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 90 (c) 17 (d) 45
  17. 17.Which term of the AP 4, 13, 22, 31, … is 265? (a) 31st (b) 30th (c) 32nd (d) 29th
  18. 18.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 136 (b) 28 (c) 133 (d) 266
  19. 19.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 85 (b) 170 (c) 25 (d) 95
  20. 20.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 1190 (c) 578 (d) 561
  21. 21.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 200 (b) 100 (c) 23 (d) 112
  22. 22.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 225 (c) 29 (d) 240
  23. 23.What is the 35th term of the AP 3, 7, 11, 15, …? (a) 139 (b) 140 (c) 136 (d) 143
  24. 24.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 19 (b) 18 (c) 17 (d) 26
  25. 25.What is the 17th term of the AP 3, 10, 17, 24, …? (a) 115 (b) 122 (c) 112 (d) 119
  26. 26.What is the 31st term of the AP 3, 7, 11, 15, …? (a) 120 (b) 124 (c) 123 (d) 127
  27. 27.What is the 32nd term of the AP 5, 12, 19, 26, …? (a) 217 (b) 229 (c) 222 (d) 224
  28. 28.Which term of the AP 12, 17, 22, 27, … is 157? (a) 31st (b) 32nd (c) 29th (d) 30th
  29. 29.What is the 37th term of the AP 5, 14, 23, 32, …? (a) 333 (b) 324 (c) 338 (d) 329
  30. 30.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 10 (b) 45 (c) 48 (d) 90
  31. 31.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 816 (b) 67 (c) 444 (d) 408
  32. 32.Which term of the AP 18, 20, 22, 24, … is 70? (a) 27th (b) 28th (c) 26th (d) 35th
  33. 33.What is the 33rd term of the AP 16, 18, 20, 22, …? (a) 66 (b) 82 (c) 64 (d) 80
  34. 34.What is the 20th term of the AP 20, 27, 34, 41, …? (a) 153 (b) 133 (c) 140 (d) 160
  35. 35.Which term of the AP 2, 11, 20, 29, … is 173? (a) 19th (b) 22nd (c) 20th (d) 21st
  36. 36.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 380 (c) 190 (d) 191
  37. 37.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 10 (b) 8 (c) 7 (d) 6
  38. 38.What is the missing term in the AP 5, 9, ?, 17, 21? (a) 17 (b) 14 (c) 12 (d) 13
  39. 39.Which term of the AP 20, 27, 34, 41, … is 237? (a) 33rd (b) 34th (c) 32nd (d) 31st
  40. 40.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 170 (b) 26 (c) 180 (d) 340

Answer key

  1. 66
  2. 74
  3. 24th
  4. 336
  5. 3570
  6. 57
  7. 252
  8. 112
  9. 128
  10. 20
  11. 100
  12. 25
  13. 20
  14. 946
  15. 361
  16. 81
  17. 30th
  18. 133
  19. 85
  20. 595
  21. 100
  22. 225
  23. 139
  24. 18
  25. 115
  26. 123
  27. 222
  28. 30th
  29. 329
  30. 45
  31. 408
  32. 27th
  33. 80
  34. 153
  35. 20th
  36. 190
  37. 7
  38. 13
  39. 32nd
  40. 170

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