Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 956 · 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 2, 4, 6, …? (a) 14 (b) 112 (c) 63 (d) 56
2. 2.What is the 22nd term of the AP 2, 7, 12, 17, …? (a) 112 (b) 110 (c) 105 (d) 107
3. 3.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 2450 (c) 4970 (d) 2485
4. 4.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 700 (b) 380 (c) 62 (d) 350
5. 5.Which term of the AP 19, 22, 25, 28, … is 52? (a) 13th (b) 12th (c) 11th (d) 14th
6. 6.What is the missing term in the AP 16, 20, 24, ?, 32? (a) 28 (b) 27 (c) 32 (d) 29
7. 7.What is the missing term in the AP 14, 20, ?, 32, 38? (a) 27 (b) 32 (c) 25 (d) 26
8. 8.What is the missing term in the AP 18, 25, 32, ?, 46? (a) 39 (b) 40 (c) 46 (d) 38
9. 9.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 147 (b) 33 (c) 294 (d) 161
10. 10.What is the 21st term of the AP 15, 22, 29, 36, …? (a) 155 (b) 140 (c) 162 (d) 147
11. 11.Which term of the AP 16, 21, 26, 31, … is 61? (a) 10th (b) 12th (c) 9th (d) 11th
12. 12.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 578 (c) 561 (d) 595
13. 13.What is the sum of the first 11 terms of the AP 3, 8, 13, …? (a) 53 (b) 313 (c) 308 (d) 616
14. 14.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 45 (d) 529
15. 15.What is the 27th term of the AP 8, 13, 18, 23, …? (a) 130 (b) 135 (c) 138 (d) 143
16. 16.What is the 35th term of the AP 5, 7, 9, 11, …? (a) 70 (b) 73 (c) 68 (d) 75
17. 17.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 3081 (c) 3042 (d) 6162
18. 18.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 450 (b) 240 (c) 36 (d) 225
19. 19.What is the missing term in the AP 20, 22, ?, 26, 28? (a) 24 (b) 23 (c) 26 (d) 25
20. 20.What is the 19th term of the AP 14, 21, 28, 35, …? (a) 140 (b) 133 (c) 147 (d) 126
21. 21.What is the missing term in the AP 1, 8, ?, 22, 29? (a) 14 (b) 15 (c) 16 (d) 22
22. 22.Which term of the AP 17, 21, 25, 29, … is 109? (a) 24th (b) 26th (c) 25th (d) 23rd
23. 23.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 432 (b) 216 (c) 228 (d) 29
24. 24.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 18 (b) 15 (c) 14 (d) 16
25. 25.What is the 37th term of the AP 5, 9, 13, 17, …? (a) 144 (b) 148 (c) 153 (d) 149
26. 26.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 24 (b) 144 (c) 272 (d) 136
27. 27.Which term of the AP 18, 23, 28, 33, … is 163? (a) 32nd (b) 31st (c) 29th (d) 30th
28. 28.Which term of the AP 7, 15, 23, 31, … is 239? (a) 29th (b) 30th (c) 32nd (d) 31st
29. 29.What is the sum of all the whole numbers from 1 to 36? (a) 630 (b) 666 (c) 648 (d) 1332
30. 30.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 470 (b) 46 (c) 235 (d) 260
31. 31.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 25 (b) 320 (c) 170 (d) 160
32. 32.Which term of the AP 1, 7, 13, 19, … is 55? (a) 11th (b) 10th (c) 9th (d) 12th
33. 33.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 39 (c) 210 (d) 420
34. 34.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 132 (d) 66
35. 35.Which term of the AP 14, 16, 18, 20, … is 52? (a) 19th (b) 21st (c) 26th (d) 20th
36. 36.What is the 37th term of the AP 19, 25, 31, 37, …? (a) 216 (b) 235 (c) 222 (d) 241
37. 37.Which term of the AP 9, 12, 15, 18, … is 99? (a) 32nd (b) 33rd (c) 30th (d) 31st
38. 38.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 2557 (c) 5112 (d) 2485
39. 39.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 9 (b) 11 (c) 14 (d) 10
40. 40.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 1560 (c) 781 (d) 741

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