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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 608 · 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 all the whole numbers from 1 to 98? (a) 9702 (b) 4851 (c) 4753 (d) 4802
  2. 2.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 75 (b) 18 (c) 140 (d) 70
  3. 3.What is the 33rd term of the AP 14, 19, 24, 29, …? (a) 165 (b) 160 (c) 179 (d) 174
  4. 4.What is the 14th term of the AP 16, 20, 24, 28, …? (a) 52 (b) 56 (c) 72 (d) 68
  5. 5.What is the 36th term of the AP 20, 28, 36, 44, …? (a) 288 (b) 300 (c) 308 (d) 280
  6. 6.What is the missing term in the AP 14, ?, 20, 23, 26? (a) 17 (b) 18 (c) 20 (d) 16
  7. 7.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 64 (b) 740 (c) 400 (d) 370
  8. 8.What is the sum of the first 10 terms of the AP 5, 10, 15, …? (a) 300 (b) 550 (c) 50 (d) 275
  9. 9.What is the 34th term of the AP 5, 8, 11, 14, …? (a) 99 (b) 102 (c) 107 (d) 104
  10. 10.What is the 24th term of the AP 16, 25, 34, 43, …? (a) 207 (b) 223 (c) 216 (d) 232
  11. 11.What is the sum of all the whole numbers from 1 to 23? (a) 277 (b) 253 (c) 552 (d) 276
  12. 12.What is the sum of the first 12 terms of the AP 10, 16, 22, …? (a) 76 (b) 552 (c) 1032 (d) 516
  13. 13.What is the 40th term of the AP 8, 14, 20, 26, …? (a) 234 (b) 242 (c) 240 (d) 248
  14. 14.Which term of the AP 11, 15, 19, 23, … is 43? (a) 8th (b) 11th (c) 10th (d) 9th
  15. 15.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 169 (d) 182
  16. 16.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 666 (c) 648 (d) 630
  17. 17.What is the 25th term of the AP 12, 19, 26, 33, …? (a) 168 (b) 175 (c) 180 (d) 187
  18. 18.What is the 31st term of the AP 15, 21, 27, 33, …? (a) 201 (b) 186 (c) 195 (d) 180
  19. 19.Which term of the AP 5, 8, 11, 14, … is 50? (a) 16th (b) 17th (c) 15th (d) 18th
  20. 20.What is the sum of all the whole numbers from 1 to 54? (a) 1485 (b) 2970 (c) 1431 (d) 1458
  21. 21.What is the 34th term of the AP 1, 4, 7, 10, …? (a) 102 (b) 100 (c) 103 (d) 99
  22. 22.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 338 (c) 702 (d) 351
  23. 23.What is the missing term in the AP 12, 21, ?, 39, 48? (a) 31 (b) 29 (c) 30 (d) 39
  24. 24.What is the missing term in the AP 11, 17, 23, ?, 35? (a) 29 (b) 35 (c) 28 (d) 30
  25. 25.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 529 (c) 552 (d) 45
  26. 26.What is the 26th term of the AP 8, 14, 20, 26, …? (a) 150 (b) 156 (c) 158 (d) 164
  27. 27.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 516 (b) 480 (c) 73 (d) 960
  28. 28.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 3486 (c) 3570 (d) 7140
  29. 29.What is the 28th term of the AP 10, 12, 14, 16, …? (a) 64 (b) 54 (c) 56 (d) 66
  30. 30.What is the 34th term of the AP 7, 16, 25, 34, …? (a) 304 (b) 313 (c) 306 (d) 297
  31. 31.Which term of the AP 17, 25, 33, 41, … is 145? (a) 16th (b) 19th (c) 17th (d) 18th
  32. 32.Which term of the AP 15, 18, 21, 24, … is 78? (a) 23rd (b) 26th (c) 22nd (d) 21st
  33. 33.What is the 19th term of the AP 8, 12, 16, 20, …? (a) 72 (b) 80 (c) 84 (d) 76
  34. 34.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 306 (d) 289
  35. 35.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 64 (d) 15
  36. 36.What is the 15th term of the AP 9, 11, 13, 15, …? (a) 39 (b) 28 (c) 30 (d) 37
  37. 37.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 308 (b) 46 (c) 286 (d) 572
  38. 38.Which term of the AP 14, 18, 22, 26, … is 62? (a) 15th (b) 13th (c) 12th (d) 14th
  39. 39.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 1190 (c) 595 (d) 561
  40. 40.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 40 (b) 564 (c) 300 (d) 282

Answer key

  1. 4851
  2. 70
  3. 174
  4. 68
  5. 300
  6. 17
  7. 370
  8. 275
  9. 104
  10. 223
  11. 276
  12. 516
  13. 242
  14. 9th
  15. 169
  16. 666
  17. 180
  18. 195
  19. 16th
  20. 1485
  21. 100
  22. 351
  23. 30
  24. 29
  25. 529
  26. 158
  27. 480
  28. 3570
  29. 64
  30. 304
  31. 17th
  32. 22nd
  33. 80
  34. 289
  35. 64
  36. 37
  37. 286
  38. 13th
  39. 595
  40. 282

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