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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 742 · 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 17, 21, ?, 29, 33? (a) 29 (b) 26 (c) 24 (d) 25
  2. 2.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 5 (b) 4 (c) 2 (d) 3
  3. 3.What is the sum of all the whole numbers from 1 to 37? (a) 666 (b) 1406 (c) 704 (d) 703
  4. 4.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 42 (b) 11 (c) 36 (d) 72
  5. 5.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1225 (c) 1176 (d) 1226
  6. 6.What is the missing term in the AP 14, 16, ?, 20, 22? (a) 19 (b) 20 (c) 17 (d) 18
  7. 7.What is the sum of the first 12 terms of the AP 9, 13, 17, …? (a) 744 (b) 396 (c) 53 (d) 372
  8. 8.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 540 (b) 270 (c) 288 (d) 39
  9. 9.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 52 (b) 279 (c) 504 (d) 252
  10. 10.What is the 14th term of the AP 17, 19, 21, 23, …? (a) 26 (b) 28 (c) 43 (d) 45
  11. 11.What is the 17th term of the AP 20, 22, 24, 26, …? (a) 54 (b) 32 (c) 52 (d) 34
  12. 12.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 1431 (c) 1378 (d) 2862
  13. 13.Which term of the AP 14, 23, 32, 41, … is 194? (a) 21st (b) 22nd (c) 23rd (d) 20th
  14. 14.What is the 15th term of the AP 3, 11, 19, 27, …? (a) 120 (b) 112 (c) 115 (d) 123
  15. 15.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 42 (c) 11 (d) 21
  16. 16.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 64 (d) 15
  17. 17.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 54 (b) 768 (c) 384 (d) 408
  18. 18.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 6 (b) 8 (c) 9 (d) 7
  19. 19.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 342 (c) 171 (d) 35
  20. 20.What is the 40th term of the AP 12, 18, 24, 30, …? (a) 234 (b) 246 (c) 240 (d) 252
  21. 21.What is the 31st term of the AP 1, 9, 17, 25, …? (a) 240 (b) 249 (c) 241 (d) 248
  22. 22.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 156 (d) 78
  23. 23.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 100 (d) 19
  24. 24.Which term of the AP 6, 13, 20, 27, … is 251? (a) 36th (b) 37th (c) 38th (d) 35th
  25. 25.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 58 (b) 306 (c) 333 (d) 612
  26. 26.What is the missing term in the AP 18, 24, ?, 36, 42? (a) 29 (b) 36 (c) 30 (d) 31
  27. 27.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 41 (b) 378 (c) 194 (d) 189
  28. 28.What is the 11th term of the AP 5, 10, 15, 20, …? (a) 50 (b) 55 (c) 56 (d) 60
  29. 29.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 238 (b) 119 (c) 32 (d) 124
  30. 30.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 70 (b) 11 (c) 65 (d) 130
  31. 31.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 47 (b) 248 (c) 486 (d) 243
  32. 32.What is the 11th term of the AP 7, 11, 15, 19, …? (a) 40 (b) 47 (c) 51 (d) 44
  33. 33.Which term of the AP 12, 20, 28, 36, … is 76? (a) 11th (b) 9th (c) 8th (d) 10th
  34. 34.What is the 12th term of the AP 11, 14, 17, 20, …? (a) 47 (b) 44 (c) 36 (d) 33
  35. 35.What is the 33rd term of the AP 2, 7, 12, 17, …? (a) 165 (b) 160 (c) 167 (d) 162
  36. 36.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 990 (c) 968 (d) 946
  37. 37.What is the 33rd term of the AP 2, 10, 18, 26, …? (a) 266 (b) 258 (c) 256 (d) 264
  38. 38.What is the 22nd term of the AP 13, 21, 29, 37, …? (a) 168 (b) 181 (c) 189 (d) 176
  39. 39.Which term of the AP 3, 6, 9, 12, … is 87? (a) 28th (b) 29th (c) 31st (d) 30th
  40. 40.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 69 (b) 432 (c) 468 (d) 864

Answer key

  1. 25
  2. 3
  3. 703
  4. 36
  5. 1225
  6. 18
  7. 372
  8. 270
  9. 252
  10. 43
  11. 52
  12. 1431
  13. 21st
  14. 115
  15. 36
  16. 64
  17. 384
  18. 7
  19. 324
  20. 246
  21. 241
  22. 144
  23. 100
  24. 36th
  25. 306
  26. 30
  27. 189
  28. 55
  29. 119
  30. 65
  31. 243
  32. 47
  33. 9th
  34. 44
  35. 162
  36. 990
  37. 258
  38. 181
  39. 29th
  40. 432

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