← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 460 · 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 10, 11, 12, …? (a) 145 (b) 290 (c) 150 (d) 19
  2. 2.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 240 (b) 35 (c) 138 (d) 120
  3. 3.Which term of the AP 19, 22, 25, 28, … is 127? (a) 39th (b) 36th (c) 37th (d) 38th
  4. 4.Which term of the AP 5, 8, 11, 14, … is 113? (a) 38th (b) 36th (c) 39th (d) 37th
  5. 5.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 166 (b) 165 (c) 20 (d) 330
  6. 6.What is the 24th term of the AP 11, 14, 17, 20, …? (a) 72 (b) 69 (c) 83 (d) 80
  7. 7.What is the 12th term of the AP 19, 26, 33, 40, …? (a) 84 (b) 103 (c) 96 (d) 77
  8. 8.What is the sum of all the whole numbers from 1 to 89? (a) 4005 (b) 8010 (c) 3916 (d) 4006
  9. 9.What is the sum of all the whole numbers from 1 to 90? (a) 4005 (b) 8190 (c) 4095 (d) 4050
  10. 10.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 650 (d) 625
  11. 11.Which term of the AP 17, 19, 21, 23, … is 71? (a) 27th (b) 29th (c) 28th (d) 30th
  12. 12.Which term of the AP 17, 21, 25, 29, … is 117? (a) 27th (b) 25th (c) 28th (d) 26th
  13. 13.What is the 40th term of the AP 7, 9, 11, 13, …? (a) 78 (b) 87 (c) 80 (d) 85
  14. 14.What is the 18th term of the AP 5, 13, 21, 29, …? (a) 144 (b) 149 (c) 141 (d) 136
  15. 15.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 8 (b) 9 (c) 6 (d) 7
  16. 16.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 240 (b) 480 (c) 252 (d) 31
  17. 17.What is the 17th term of the AP 20, 28, 36, 44, …? (a) 148 (b) 128 (c) 156 (d) 136
  18. 18.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 396 (b) 203 (c) 198 (d) 42
  19. 19.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 14 (b) 12 (c) 16 (d) 13
  20. 20.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 198 (b) 396 (c) 38 (d) 216
  21. 21.What is the 33rd term of the AP 14, 17, 20, 23, …? (a) 99 (b) 113 (c) 110 (d) 96
  22. 22.What is the 36th term of the AP 5, 12, 19, 26, …? (a) 252 (b) 245 (c) 257 (d) 250
  23. 23.Which term of the AP 1, 5, 9, 13, … is 89? (a) 24th (b) 22nd (c) 25th (d) 23rd
  24. 24.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1225 (c) 1226 (d) 1176
  25. 25.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 70 (b) 19 (c) 73 (d) 140
  26. 26.What is the 12th term of the AP 11, 16, 21, 26, …? (a) 55 (b) 66 (c) 71 (d) 60
  27. 27.What is the 10th term of the AP 9, 17, 25, 33, …? (a) 89 (b) 81 (c) 80 (d) 72
  28. 28.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 703 (c) 722 (d) 1482
  29. 29.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 11 (b) 65 (c) 130 (d) 70
  30. 30.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 144 (b) 288 (c) 147 (d) 28
  31. 31.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 36 (c) 42 (d) 11
  32. 32.What is the 26th term of the AP 18, 23, 28, 33, …? (a) 143 (b) 130 (c) 148 (d) 125
  33. 33.What is the 40th term of the AP 1, 3, 5, 7, …? (a) 81 (b) 80 (c) 79 (d) 78
  34. 34.What is the 13th term of the AP 8, 11, 14, 17, …? (a) 44 (b) 39 (c) 47 (d) 36
  35. 35.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 55 (b) 110 (c) 15 (d) 60
  36. 36.Which term of the AP 4, 13, 22, 31, … is 274? (a) 30th (b) 32nd (c) 31st (d) 33rd
  37. 37.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4950 (c) 4851 (d) 9900
  38. 38.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 25 (d) 30
  39. 39.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1432 (c) 1378 (d) 1431
  40. 40.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4560 (c) 4656 (d) 4608

Answer key

  1. 145
  2. 120
  3. 37th
  4. 37th
  5. 165
  6. 80
  7. 96
  8. 4005
  9. 4095
  10. 625
  11. 28th
  12. 26th
  13. 85
  14. 141
  15. 7
  16. 240
  17. 148
  18. 198
  19. 13
  20. 198
  21. 110
  22. 250
  23. 23rd
  24. 1225
  25. 70
  26. 66
  27. 81
  28. 741
  29. 65
  30. 144
  31. 36
  32. 143
  33. 79
  34. 44
  35. 55
  36. 31st
  37. 4950
  38. 25
  39. 1431
  40. 4656

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