← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 934 · 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 7 terms of the AP 9, 14, 19, …? (a) 168 (b) 173 (c) 39 (d) 336
  2. 2.What is the 30th term of the AP 5, 10, 15, 20, …? (a) 155 (b) 151 (c) 150 (d) 145
  3. 3.What is the 39th term of the AP 5, 11, 17, 23, …? (a) 239 (b) 228 (c) 233 (d) 234
  4. 4.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 2485 (c) 5112 (d) 2557
  5. 5.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 1980 (c) 968 (d) 946
  6. 6.Which term of the AP 6, 8, 10, 12, … is 22? (a) 9th (b) 8th (c) 11th (d) 10th
  7. 7.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 16 (b) 5 (c) 15 (d) 30
  8. 8.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 26 (b) 70 (c) 140 (d) 85
  9. 9.Which term of the AP 20, 26, 32, 38, … is 188? (a) 31st (b) 28th (c) 29th (d) 30th
  10. 10.Which term of the AP 6, 11, 16, 21, … is 186? (a) 37th (b) 36th (c) 38th (d) 39th
  11. 11.What is the missing term in the AP 5, 8, ?, 14, 17? (a) 11 (b) 14 (c) 10 (d) 12
  12. 12.Which term of the AP 7, 9, 11, 13, … is 25? (a) 9th (b) 10th (c) 11th (d) 12th
  13. 13.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 56 (c) 28 (d) 13
  14. 14.What is the missing term in the AP 15, 21, ?, 33, 39? (a) 28 (b) 27 (c) 33 (d) 26
  15. 15.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 108 (b) 28 (c) 120 (d) 216
  16. 16.What is the 25th term of the AP 20, 24, 28, 32, …? (a) 116 (b) 100 (c) 120 (d) 96
  17. 17.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 65 (b) 110 (c) 19 (d) 55
  18. 18.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 88 (b) 176 (c) 89 (d) 13
  19. 19.What is the 17th term of the AP 8, 12, 16, 20, …? (a) 64 (b) 76 (c) 68 (d) 72
  20. 20.Which term of the AP 12, 20, 28, 36, … is 172? (a) 22nd (b) 20th (c) 23rd (d) 21st
  21. 21.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 406 (d) 784
  22. 22.What is the 35th term of the AP 6, 8, 10, 12, …? (a) 76 (b) 68 (c) 74 (d) 70
  23. 23.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 380 (c) 190 (d) 191
  24. 24.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 168 (b) 294 (c) 147 (d) 39
  25. 25.Which term of the AP 20, 27, 34, 41, … is 195? (a) 26th (b) 28th (c) 27th (d) 25th
  26. 26.What is the 33rd term of the AP 13, 17, 21, 25, …? (a) 132 (b) 128 (c) 141 (d) 145
  27. 27.What is the missing term in the AP 16, ?, 32, 40, 48? (a) 23 (b) 25 (c) 32 (d) 24
  28. 28.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 374 (b) 32 (c) 187 (d) 190
  29. 29.What is the sum of the first 7 terms of the AP 7, 12, 17, …? (a) 159 (b) 37 (c) 308 (d) 154
  30. 30.Which term of the AP 3, 7, 11, 15, … is 147? (a) 39th (b) 38th (c) 36th (d) 37th
  31. 31.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 4951 (c) 9900 (d) 4851
  32. 32.What is the sum of the first 9 terms of the AP 5, 7, 9, …? (a) 234 (b) 126 (c) 117 (d) 21
  33. 33.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 4560 (c) 4656 (d) 9312
  34. 34.Which term of the AP 16, 21, 26, 31, … is 96? (a) 16th (b) 19th (c) 17th (d) 18th
  35. 35.What is the 20th term of the AP 16, 19, 22, 25, …? (a) 57 (b) 76 (c) 73 (d) 60
  36. 36.What is the 28th term of the AP 4, 9, 14, 19, …? (a) 140 (b) 139 (c) 144 (d) 135
  37. 37.What is the 23rd term of the AP 17, 23, 29, 35, …? (a) 132 (b) 155 (c) 138 (d) 149
  38. 38.What is the 13th term of the AP 3, 11, 19, 27, …? (a) 96 (b) 107 (c) 104 (d) 99
  39. 39.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 144 (b) 23 (c) 288 (d) 156
  40. 40.What is the 18th term of the AP 4, 8, 12, 16, …? (a) 72 (b) 68 (c) 73 (d) 76

Answer key

  1. 168
  2. 150
  3. 233
  4. 2556
  5. 990
  6. 9th
  7. 15
  8. 70
  9. 29th
  10. 37th
  11. 11
  12. 10th
  13. 49
  14. 27
  15. 108
  16. 116
  17. 55
  18. 88
  19. 72
  20. 21st
  21. 784
  22. 74
  23. 190
  24. 147
  25. 26th
  26. 141
  27. 24
  28. 187
  29. 154
  30. 37th
  31. 4950
  32. 117
  33. 4656
  34. 17th
  35. 73
  36. 139
  37. 149
  38. 99
  39. 144
  40. 72

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