Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 402 · 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 sum of the first 7 terms of the AP 7, 9, 11, …? (a) 91 (b) 19 (c) 182 (d) 98
2. 2.What is the 24th term of the AP 12, 19, 26, 33, …? (a) 161 (b) 180 (c) 173 (d) 168
3. 3.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 9 (b) 7 (c) 8 (d) 14
4. 4.What is the 25th term of the AP 19, 25, 31, 37, …? (a) 150 (b) 169 (c) 163 (d) 144
5. 5.Which term of the AP 7, 12, 17, 22, … is 147? (a) 28th (b) 30th (c) 31st (d) 29th
6. 6.What is the sum of all the whole numbers from 1 to 50? (a) 1225 (b) 2550 (c) 1275 (d) 1250
7. 7.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 9900 (c) 4951 (d) 4851
8. 8.What is the missing term in the AP 12, 19, 26, ?, 40? (a) 32 (b) 34 (c) 33 (d) 40
9. 9.What is the 22nd term of the AP 18, 26, 34, 42, …? (a) 194 (b) 168 (c) 176 (d) 186
10. 10.What is the 15th term of the AP 16, 18, 20, 22, …? (a) 30 (b) 44 (c) 46 (d) 28
11. 11.What is the missing term in the AP 18, ?, 22, 24, 26? (a) 19 (b) 20 (c) 22 (d) 21
12. 12.What is the 27th term of the AP 5, 13, 21, 29, …? (a) 221 (b) 216 (c) 208 (d) 213
13. 13.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 66 (c) 121 (d) 21
14. 14.What is the missing term in the AP 17, 26, 35, ?, 53? (a) 45 (b) 53 (c) 44 (d) 43
15. 15.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1352 (c) 1378 (d) 1326
16. 16.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 132 (b) 252 (c) 16 (d) 126
17. 17.Which term of the AP 19, 21, 23, 25, … is 73? (a) 30th (b) 29th (c) 28th (d) 27th
18. 18.What is the sum of all the whole numbers from 1 to 82? (a) 6806 (b) 3362 (c) 3403 (d) 3321
19. 19.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 240 (d) 225
20. 20.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 121 (c) 120 (d) 240
21. 21.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 88 (b) 48 (c) 9 (d) 44
22. 22.What is the 25th term of the AP 10, 12, 14, 16, …? (a) 60 (b) 50 (c) 58 (d) 48
23. 23.What is the 24th term of the AP 6, 13, 20, 27, …? (a) 168 (b) 167 (c) 174 (d) 161
24. 24.What is the 28th term of the AP 13, 18, 23, 28, …? (a) 148 (b) 153 (c) 135 (d) 140
25. 25.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 72 (b) 68 (c) 12 (d) 136
26. 26.Which term of the AP 2, 8, 14, 20, … is 206? (a) 36th (b) 37th (c) 34th (d) 35th
27. 27.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 19 (d) 100
28. 28.What is the 23rd term of the AP 4, 6, 8, 10, …? (a) 44 (b) 46 (c) 48 (d) 50
29. 29.What is the 13th term of the AP 17, 22, 27, 32, …? (a) 82 (b) 60 (c) 77 (d) 65
30. 30.What is the 33rd term of the AP 4, 6, 8, 10, …? (a) 64 (b) 66 (c) 68 (d) 70
31. 31.What is the 28th term of the AP 4, 13, 22, 31, …? (a) 247 (b) 256 (c) 252 (d) 243
32. 32.What is the 12th term of the AP 12, 17, 22, 27, …? (a) 72 (b) 60 (c) 55 (d) 67
33. 33.What is the sum of all the whole numbers from 1 to 14? (a) 105 (b) 91 (c) 210 (d) 98
34. 34.Which term of the AP 16, 20, 24, 28, … is 124? (a) 31st (b) 29th (c) 27th (d) 28th
35. 35.What is the missing term in the AP 1, ?, 9, 13, 17? (a) 9 (b) 6 (c) 5 (d) 4
36. 36.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 578 (c) 595 (d) 561
37. 37.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 10 (b) 8 (c) 9 (d) 15
38. 38.What is the 17th term of the AP 15, 21, 27, 33, …? (a) 117 (b) 96 (c) 102 (d) 111
39. 39.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 1711 (c) 1682 (d) 3422
40. 40.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 19 (b) 17 (c) 18 (d) 22

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