Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 672 · 40 questions

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.

1. 1.What is the 27th term of the AP 11, 20, 29, 38, …? (a) 254 (b) 245 (c) 243 (d) 234
2. 2.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 39 (b) 294 (c) 168 (d) 147
3. 3.Which term of the AP 6, 10, 14, 18, … is 114? (a) 30th (b) 29th (c) 27th (d) 28th
4. 4.What is the 10th term of the AP 14, 18, 22, 26, …? (a) 40 (b) 50 (c) 54 (d) 36
5. 5.Which term of the AP 4, 11, 18, 25, … is 214? (a) 33rd (b) 32nd (c) 30th (d) 31st
6. 6.What is the missing term in the AP 11, 15, ?, 23, 27? (a) 23 (b) 20 (c) 19 (d) 18
7. 7.What is the 39th term of the AP 7, 12, 17, 22, …? (a) 195 (b) 197 (c) 190 (d) 202
8. 8.Which term of the AP 19, 24, 29, 34, … is 159? (a) 31st (b) 30th (c) 29th (d) 28th
9. 9.What is the 26th term of the AP 1, 4, 7, 10, …? (a) 76 (b) 75 (c) 78 (d) 79
10. 10.What is the missing term in the AP 7, 10, 13, ?, 19? (a) 16 (b) 15 (c) 17 (d) 19
11. 11.What is the 34th term of the AP 20, 28, 36, 44, …? (a) 264 (b) 272 (c) 292 (d) 284
12. 12.Which term of the AP 8, 10, 12, 14, … is 38? (a) 17th (b) 19th (c) 15th (d) 16th
13. 13.Which term of the AP 3, 10, 17, 24, … is 248? (a) 35th (b) 37th (c) 38th (d) 36th
14. 14.What is the missing term in the AP 6, 9, ?, 15, 18? (a) 11 (b) 13 (c) 15 (d) 12
15. 15.What is the 17th term of the AP 18, 24, 30, 36, …? (a) 102 (b) 120 (c) 114 (d) 96
16. 16.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 25 (d) 169
17. 17.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 49 (d) 56
18. 18.What is the 31st term of the AP 9, 16, 23, 30, …? (a) 210 (b) 219 (c) 217 (d) 226
19. 19.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 2070 (c) 1035 (d) 990
20. 20.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 210 (b) 114 (c) 25 (d) 105
21. 21.Which term of the AP 17, 26, 35, 44, … is 206? (a) 24th (b) 21st (c) 22nd (d) 23rd
22. 22.Which term of the AP 14, 17, 20, 23, … is 56? (a) 16th (b) 14th (c) 17th (d) 15th
23. 23.What is the 20th term of the AP 2, 8, 14, 20, …? (a) 114 (b) 122 (c) 116 (d) 120
24. 24.What is the sum of all the whole numbers from 1 to 27? (a) 378 (b) 379 (c) 756 (d) 351
25. 25.What is the 26th term of the AP 2, 6, 10, 14, …? (a) 106 (b) 104 (c) 100 (d) 102
26. 26.What is the 33rd term of the AP 1, 5, 9, 13, …? (a) 128 (b) 129 (c) 133 (d) 132
27. 27.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 44 (b) 34 (c) 35 (d) 36
28. 28.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 900 (c) 465 (d) 59
29. 29.What is the 26th term of the AP 3, 11, 19, 27, …? (a) 200 (b) 208 (c) 203 (d) 211
30. 30.Which term of the AP 4, 9, 14, 19, … is 164? (a) 32nd (b) 34th (c) 35th (d) 33rd
31. 31.What is the 13th term of the AP 20, 26, 32, 38, …? (a) 98 (b) 78 (c) 92 (d) 72
32. 32.What is the 27th term of the AP 14, 23, 32, 41, …? (a) 257 (b) 234 (c) 243 (d) 248
33. 33.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 10 (b) 5 (c) 7 (d) 6
34. 34.What is the 24th term of the AP 3, 8, 13, 18, …? (a) 115 (b) 118 (c) 123 (d) 120
35. 35.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 13 (b) 56 (c) 49 (d) 98
36. 36.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 50 (c) 110 (d) 45
37. 37.Which term of the AP 4, 7, 10, 13, … is 67? (a) 23rd (b) 21st (c) 22nd (d) 24th
38. 38.What is the missing term in the AP 5, ?, 15, 20, 25? (a) 10 (b) 15 (c) 9 (d) 11
39. 39.What is the 27th term of the AP 18, 20, 22, 24, …? (a) 54 (b) 52 (c) 70 (d) 72
40. 40.What is the 17th term of the AP 12, 18, 24, 30, …? (a) 108 (b) 114 (c) 102 (d) 96

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