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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 963 · 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 1, 3, 5, …? (a) 19 (b) 200 (c) 110 (d) 100
  2. 2.What is the 14th term of the AP 17, 25, 33, 41, …? (a) 121 (b) 112 (c) 129 (d) 104
  3. 3.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 18 (b) 75 (c) 70 (d) 140
  4. 4.What is the missing term in the AP 3, 11, 19, ?, 35? (a) 28 (b) 27 (c) 26 (d) 35
  5. 5.Which term of the AP 20, 28, 36, 44, … is 228? (a) 29th (b) 26th (c) 27th (d) 28th
  6. 6.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2211 (c) 2178 (d) 2145
  7. 7.Which term of the AP 9, 16, 23, 30, … is 93? (a) 13th (b) 14th (c) 15th (d) 12th
  8. 8.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 100 (d) 19
  9. 9.What is the 23rd term of the AP 6, 11, 16, 21, …? (a) 116 (b) 110 (c) 121 (d) 115
  10. 10.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 35 (b) 30 (c) 60 (d) 10
  11. 11.What is the 11th term of the AP 6, 11, 16, 21, …? (a) 61 (b) 55 (c) 56 (d) 50
  12. 12.Which term of the AP 11, 16, 21, 26, … is 206? (a) 41st (b) 40th (c) 42nd (d) 39th
  13. 13.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 300 (c) 276 (d) 600
  14. 14.What is the missing term in the AP 11, ?, 29, 38, 47? (a) 20 (b) 29 (c) 19 (d) 21
  15. 15.What is the 24th term of the AP 14, 23, 32, 41, …? (a) 216 (b) 207 (c) 221 (d) 230
  16. 16.What is the 18th term of the AP 3, 10, 17, 24, …? (a) 122 (b) 126 (c) 119 (d) 129
  17. 17.What is the 17th term of the AP 12, 19, 26, 33, …? (a) 119 (b) 124 (c) 112 (d) 131
  18. 18.What is the 37th term of the AP 20, 29, 38, 47, …? (a) 333 (b) 353 (c) 324 (d) 344
  19. 19.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4656 (c) 9506 (d) 4753
  20. 20.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 465 (c) 59 (d) 930
  21. 21.Which term of the AP 3, 9, 15, 21, … is 129? (a) 23rd (b) 24th (c) 21st (d) 22nd
  22. 22.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 190 (c) 361 (d) 37
  23. 23.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 99 (b) 14 (c) 100 (d) 198
  24. 24.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 192 (b) 108 (c) 96 (d) 26
  25. 25.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 276 (d) 45
  26. 26.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 7140 (c) 3570 (d) 3528
  27. 27.What is the missing term in the AP 6, 15, 24, ?, 42? (a) 34 (b) 33 (c) 32 (d) 42
  28. 28.What is the 12th term of the AP 3, 12, 21, 30, …? (a) 108 (b) 99 (c) 111 (d) 102
  29. 29.What is the 38th term of the AP 9, 15, 21, 27, …? (a) 228 (b) 222 (c) 231 (d) 237
  30. 30.Which term of the AP 1, 9, 17, 25, … is 257? (a) 33rd (b) 34th (c) 35th (d) 32nd
  31. 31.What is the 27th term of the AP 6, 14, 22, 30, …? (a) 222 (b) 214 (c) 216 (d) 208
  32. 32.What is the 38th term of the AP 6, 15, 24, 33, …? (a) 348 (b) 342 (c) 333 (d) 339
  33. 33.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 595 (c) 561 (d) 578
  34. 34.What is the sum of all the whole numbers from 1 to 67? (a) 4556 (b) 2279 (c) 2278 (d) 2211
  35. 35.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4560 (c) 4656 (d) 4608
  36. 36.Which term of the AP 9, 14, 19, 24, … is 204? (a) 41st (b) 40th (c) 42nd (d) 39th
  37. 37.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 903 (c) 946 (d) 947
  38. 38.What is the sum of the first 10 terms of the AP 9, 13, 17, …? (a) 540 (b) 290 (c) 45 (d) 270
  39. 39.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 6 (b) 7 (c) 8 (d) 9
  40. 40.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 168 (b) 162 (c) 324 (d) 19

Answer key

  1. 100
  2. 121
  3. 70
  4. 27
  5. 27th
  6. 2211
  7. 13th
  8. 100
  9. 116
  10. 30
  11. 56
  12. 40th
  13. 300
  14. 20
  15. 221
  16. 122
  17. 124
  18. 344
  19. 4753
  20. 900
  21. 22nd
  22. 361
  23. 99
  24. 96
  25. 529
  26. 3570
  27. 33
  28. 102
  29. 231
  30. 33rd
  31. 214
  32. 339
  33. 595
  34. 2278
  35. 4656
  36. 40th
  37. 946
  38. 270
  39. 7
  40. 162

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