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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 496 · 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.Which term of the AP 14, 19, 24, 29, … is 204? (a) 41st (b) 38th (c) 40th (d) 39th
  2. 2.Which term of the AP 10, 19, 28, 37, … is 361? (a) 41st (b) 40th (c) 42nd (d) 39th
  3. 3.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 5112 (c) 2557 (d) 2556
  4. 4.What is the 20th term of the AP 5, 14, 23, 32, …? (a) 171 (b) 176 (c) 180 (d) 185
  5. 5.What is the missing term in the AP 7, 15, ?, 31, 39? (a) 22 (b) 23 (c) 31 (d) 24
  6. 6.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 468 (b) 72 (c) 504 (d) 936
  7. 7.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 195 (b) 390 (c) 33 (d) 210
  8. 8.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 322 (b) 161 (c) 182 (d) 41
  9. 9.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 276 (c) 552 (d) 45
  10. 10.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 277 (c) 552 (d) 276
  11. 11.What is the missing term in the AP 13, ?, 23, 28, 33? (a) 19 (b) 17 (c) 18 (d) 23
  12. 12.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 20 (b) 21 (c) 24 (d) 19
  13. 13.What is the 38th term of the AP 18, 22, 26, 30, …? (a) 148 (b) 170 (c) 152 (d) 166
  14. 14.What is the missing term in the AP 12, 14, 16, ?, 20? (a) 17 (b) 20 (c) 18 (d) 19
  15. 15.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 300 (c) 650 (d) 325
  16. 16.What is the sum of all the whole numbers from 1 to 49? (a) 1226 (b) 2450 (c) 1176 (d) 1225
  17. 17.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 59 (c) 465 (d) 900
  18. 18.What is the 19th term of the AP 18, 20, 22, 24, …? (a) 56 (b) 38 (c) 36 (d) 54
  19. 19.What is the 29th term of the AP 4, 6, 8, 10, …? (a) 58 (b) 60 (c) 56 (d) 62
  20. 20.What is the 10th term of the AP 6, 8, 10, 12, …? (a) 18 (b) 20 (c) 24 (d) 26
  21. 21.What is the 30th term of the AP 5, 13, 21, 29, …? (a) 240 (b) 237 (c) 245 (d) 232
  22. 22.Which term of the AP 15, 19, 23, 27, … is 167? (a) 39th (b) 38th (c) 40th (d) 41st
  23. 23.What is the 26th term of the AP 18, 20, 22, 24, …? (a) 70 (b) 52 (c) 50 (d) 68
  24. 24.What is the sum of all the whole numbers from 1 to 24? (a) 600 (b) 288 (c) 300 (d) 276
  25. 25.What is the missing term in the AP 4, 13, 22, ?, 40? (a) 40 (b) 30 (c) 31 (d) 32
  26. 26.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 65 (b) 17 (c) 130 (d) 70
  27. 27.Which term of the AP 13, 15, 17, 19, … is 43? (a) 18th (b) 15th (c) 16th (d) 17th
  28. 28.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 40 (b) 41 (c) 80 (d) 10
  29. 29.What is the 32nd term of the AP 4, 9, 14, 19, …? (a) 155 (b) 159 (c) 160 (d) 164
  30. 30.What is the sum of all the whole numbers from 1 to 32? (a) 528 (b) 512 (c) 1056 (d) 496
  31. 31.Which term of the AP 12, 21, 30, 39, … is 336? (a) 38th (b) 37th (c) 39th (d) 36th
  32. 32.What is the 17th term of the AP 6, 15, 24, 33, …? (a) 159 (b) 153 (c) 144 (d) 150
  33. 33.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 156 (b) 168 (c) 312 (d) 30
  34. 34.What is the sum of all the whole numbers from 1 to 48? (a) 1152 (b) 1176 (c) 2352 (d) 1128
  35. 35.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 124 (b) 119 (c) 32 (d) 238
  36. 36.What is the 15th term of the AP 9, 11, 13, 15, …? (a) 30 (b) 37 (c) 28 (d) 39
  37. 37.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 1035 (c) 2070 (d) 990
  38. 38.What is the 26th term of the AP 12, 17, 22, 27, …? (a) 137 (b) 130 (c) 125 (d) 142
  39. 39.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4656 (c) 4608 (d) 4560
  40. 40.Which term of the AP 18, 24, 30, 36, … is 84? (a) 13th (b) 11th (c) 14th (d) 12th

Answer key

  1. 39th
  2. 40th
  3. 2556
  4. 176
  5. 23
  6. 468
  7. 195
  8. 161
  9. 529
  10. 276
  11. 18
  12. 20
  13. 166
  14. 18
  15. 325
  16. 1225
  17. 900
  18. 54
  19. 60
  20. 24
  21. 237
  22. 39th
  23. 68
  24. 300
  25. 31
  26. 65
  27. 16th
  28. 40
  29. 159
  30. 528
  31. 37th
  32. 150
  33. 156
  34. 1176
  35. 119
  36. 37
  37. 1035
  38. 137
  39. 4656
  40. 12th

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