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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 45 · 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 missing term in the AP 20, 22, 24, ?, 28? (a) 27 (b) 28 (c) 26 (d) 25
  2. 2.What is the sum of all the whole numbers from 1 to 89? (a) 3916 (b) 8010 (c) 4005 (d) 4006
  3. 3.What is the missing term in the AP 18, 21, ?, 27, 30? (a) 27 (b) 23 (c) 24 (d) 25
  4. 4.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 352 (b) 36 (c) 192 (d) 176
  5. 5.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 67 (b) 408 (c) 444 (d) 816
  6. 6.What is the 33rd term of the AP 19, 27, 35, 43, …? (a) 256 (b) 275 (c) 264 (d) 283
  7. 7.Which term of the AP 5, 13, 21, 29, … is 309? (a) 38th (b) 39th (c) 41st (d) 40th
  8. 8.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 324 (b) 57 (c) 297 (d) 594
  9. 9.What is the 16th term of the AP 10, 14, 18, 22, …? (a) 74 (b) 60 (c) 70 (d) 64
  10. 10.What is the 17th term of the AP 2, 6, 10, 14, …? (a) 64 (b) 68 (c) 66 (d) 70
  11. 11.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2415 (c) 4970 (d) 2485
  12. 12.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 900 (c) 465 (d) 59
  13. 13.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 117 (b) 234 (c) 32 (d) 132
  14. 14.What is the missing term in the AP 10, 14, 18, ?, 26? (a) 26 (b) 23 (c) 22 (d) 21
  15. 15.Which term of the AP 8, 16, 24, 32, … is 184? (a) 24th (b) 25th (c) 23rd (d) 22nd
  16. 16.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 342 (d) 324
  17. 17.What is the missing term in the AP 17, 19, ?, 23, 25? (a) 23 (b) 22 (c) 20 (d) 21
  18. 18.What is the 25th term of the AP 1, 4, 7, 10, …? (a) 75 (b) 76 (c) 72 (d) 73
  19. 19.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 390 (b) 210 (c) 195 (d) 33
  20. 20.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 378 (c) 392 (d) 406
  21. 21.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 190 (d) 37
  22. 22.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 132 (d) 121
  23. 23.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 49 (c) 325 (d) 625
  24. 24.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 6972 (c) 3486 (d) 3403
  25. 25.What is the 16th term of the AP 19, 21, 23, 25, …? (a) 49 (b) 51 (c) 30 (d) 32
  26. 26.What is the 11th term of the AP 6, 9, 12, 15, …? (a) 33 (b) 39 (c) 36 (d) 30
  27. 27.Which term of the AP 4, 12, 20, 28, … is 172? (a) 21st (b) 24th (c) 23rd (d) 22nd
  28. 28.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 550 (b) 275 (c) 40 (d) 278
  29. 29.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 96 (b) 18 (c) 88 (d) 176
  30. 30.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 12 (b) 50 (c) 51 (d) 100
  31. 31.What is the 27th term of the AP 20, 26, 32, 38, …? (a) 182 (b) 156 (c) 162 (d) 176
  32. 32.What is the missing term in the AP 7, 11, 15, ?, 23? (a) 20 (b) 23 (c) 19 (d) 18
  33. 33.What is the 37th term of the AP 20, 22, 24, 26, …? (a) 74 (b) 92 (c) 72 (d) 94
  34. 34.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 133 (b) 154 (c) 266 (d) 37
  35. 35.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 186 (b) 21 (c) 192 (d) 372
  36. 36.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 2556 (c) 5256 (d) 2628
  37. 37.Which term of the AP 6, 8, 10, 12, … is 38? (a) 16th (b) 17th (c) 19th (d) 18th
  38. 38.What is the 12th term of the AP 19, 24, 29, 34, …? (a) 60 (b) 79 (c) 74 (d) 55
  39. 39.What is the missing term in the AP 4, ?, 22, 31, 40? (a) 22 (b) 12 (c) 14 (d) 13
  40. 40.Which term of the AP 2, 10, 18, 26, … is 170? (a) 21st (b) 23rd (c) 24th (d) 22nd

Answer key

  1. 26
  2. 4005
  3. 24
  4. 176
  5. 408
  6. 275
  7. 39th
  8. 297
  9. 70
  10. 66
  11. 2485
  12. 900
  13. 117
  14. 22
  15. 23rd
  16. 324
  17. 21
  18. 73
  19. 195
  20. 406
  21. 361
  22. 121
  23. 625
  24. 3486
  25. 49
  26. 36
  27. 22nd
  28. 275
  29. 88
  30. 50
  31. 176
  32. 19
  33. 92
  34. 133
  35. 186
  36. 2628
  37. 17th
  38. 74
  39. 13
  40. 22nd

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