← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 948 · 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 12 terms of the AP 10, 16, 22, …? (a) 552 (b) 516 (c) 76 (d) 1032
  2. 2.What is the missing term in the AP 18, ?, 24, 27, 30? (a) 20 (b) 24 (c) 21 (d) 22
  3. 3.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 46 (b) 36 (c) 38 (d) 37
  4. 4.What is the missing term in the AP 14, ?, 18, 20, 22? (a) 16 (b) 17 (c) 18 (d) 15
  5. 5.What is the 11th term of the AP 9, 16, 23, 30, …? (a) 70 (b) 77 (c) 86 (d) 79
  6. 6.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 35 (d) 324
  7. 7.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 160 (b) 29 (c) 296 (d) 148
  8. 8.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 230 (b) 115 (c) 16 (d) 120
  9. 9.What is the 37th term of the AP 3, 8, 13, 18, …? (a) 180 (b) 185 (c) 188 (d) 183
  10. 10.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 3081 (c) 3003 (d) 6162
  11. 11.What is the missing term in the AP 12, 16, ?, 24, 28? (a) 20 (b) 19 (c) 24 (d) 21
  12. 12.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 55 (b) 60 (c) 10 (d) 110
  13. 13.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 56 (c) 13 (d) 28
  14. 14.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 21 (b) 150 (c) 75 (d) 78
  15. 15.What is the 24th term of the AP 19, 25, 31, 37, …? (a) 138 (b) 157 (c) 163 (d) 144
  16. 16.What is the 20th term of the AP 9, 14, 19, 24, …? (a) 100 (b) 95 (c) 104 (d) 109
  17. 17.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 19 (b) 23 (c) 21 (d) 20
  18. 18.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 162 (b) 168 (c) 324 (d) 19
  19. 19.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
  20. 20.What is the sum of all the whole numbers from 1 to 65? (a) 2146 (b) 2080 (c) 2145 (d) 4290
  21. 21.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 72 (b) 14 (c) 69 (d) 138
  22. 22.What is the 40th term of the AP 15, 20, 25, 30, …? (a) 195 (b) 210 (c) 200 (d) 215
  23. 23.What is the missing term in the AP 9, 18, ?, 36, 45? (a) 36 (b) 28 (c) 26 (d) 27
  24. 24.What is the 21st term of the AP 8, 12, 16, 20, …? (a) 88 (b) 84 (c) 80 (d) 92
  25. 25.What is the sum of the first 12 terms of the AP 5, 9, 13, …? (a) 49 (b) 348 (c) 648 (d) 324
  26. 26.What is the 23rd term of the AP 20, 26, 32, 38, …? (a) 158 (b) 132 (c) 138 (d) 152
  27. 27.Which term of the AP 18, 27, 36, 45, … is 126? (a) 15th (b) 14th (c) 13th (d) 12th
  28. 28.What is the 38th term of the AP 11, 18, 25, 32, …? (a) 270 (b) 277 (c) 259 (d) 266
  29. 29.Which term of the AP 8, 10, 12, 14, … is 54? (a) 24th (b) 23rd (c) 25th (d) 27th
  30. 30.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 1482 (c) 741 (d) 703
  31. 31.Which term of the AP 2, 8, 14, 20, … is 80? (a) 15th (b) 14th (c) 16th (d) 13th
  32. 32.What is the 31st term of the AP 17, 26, 35, 44, …? (a) 270 (b) 279 (c) 296 (d) 287
  33. 33.What is the 15th term of the AP 5, 12, 19, 26, …? (a) 105 (b) 98 (c) 103 (d) 110
  34. 34.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 180 (b) 360 (c) 27 (d) 190
  35. 35.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 253 (c) 277 (d) 276
  36. 36.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 180 (b) 360 (c) 200 (d) 40
  37. 37.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 300 (b) 280 (c) 46 (d) 560
  38. 38.What is the missing term in the AP 19, 27, 35, ?, 51? (a) 42 (b) 43 (c) 51 (d) 44
  39. 39.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 36 (d) 11
  40. 40.What is the sum of all the whole numbers from 1 to 68? (a) 2278 (b) 2346 (c) 2312 (d) 4692

Answer key

  1. 516
  2. 21
  3. 37
  4. 16
  5. 79
  6. 324
  7. 148
  8. 115
  9. 183
  10. 3081
  11. 20
  12. 55
  13. 49
  14. 75
  15. 157
  16. 104
  17. 20
  18. 162
  19. 100
  20. 2145
  21. 69
  22. 210
  23. 27
  24. 88
  25. 324
  26. 152
  27. 13th
  28. 270
  29. 24th
  30. 741
  31. 14th
  32. 287
  33. 103
  34. 180
  35. 276
  36. 180
  37. 280
  38. 43
  39. 36
  40. 2346

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad