ARITHMETIC PROGRESSION S 1. If the th p term of an A.P. be q and th q term be p , then its th r term will be (a) r q p + + (b) r q p − + (c) q r p − + (d) r q p − − 2. The sum of integers from 1 to 100 that are divisible by 2 or 5 is (a) 3000 (b) 3050 (c) 4050 (d) None of these 3. If 1 3 , 8 , 2 + + x x x are in A.P., then the value of x will be (a) 3 (b) 7 (c) 5 (d) – 2 4. If the th 9 term of an A.P. is 35 and th 19 is 75, then its th 20 terms will be (a) 78 (b) 79 (c) 80 (d) 81 5. If th n terms of two A.P.'s are 8 3 + n and 15 7 + n , then the ratio of their th 12 terms will be (a) 4/9 (b) 7/16 (c) 3/7 (d) 8/15 6. If ) 2 ( 1 , 2 1 2 1 − = = = − n a a a a n n , then 5 a is (a) 1 (b) 1 − (c) 0 (d) 2 − 7. If the numbers e d c b a , , , , form an A.P., then the value of e d c b a + − + − 4 6 4 is (a) 1 (b) 2 (c) 0 (d) None of these 8. If p times the th p term of an A.P. is equal to q times the th q term of an A.P., then th q p ) ( + term is (a) 0 (b) 1 (c) 2 (d) 3 9. The sums of n terms of two arithmetic series are in the ratio 5 6 : 3 2 + + n n , then the ratio of their th 13 terms is (a) 53 : 155 (b) 27 : 77 (c) 29 : 83 (d) 31 : 89 10. If e d c b a , , , , are in A.P. then the value of c b a 4 + + e d + − 4 in terms of a , if possible is (a) 4 a (b) 2 a (c) 3 (d) None of these 11. The sum of the series ........ 6 1 3 1 2 1 + + + to 9 terms is (a) 6 5 − (b) 2 1 − (c) 1 (d) 2 3 − 12. If the th p term of an A.P. be q 1 and th q term be p 1 , then the sum of its th pq terms will be (a) 2 1 − pq (b) 2 1 pq − (c) 2 1 + pq (d) 2 1 + − pq 13. The sum of first n natural numbers is (a) ) 1 ( − n n (b) 2 ) 1 ( − n n (c) ) 1 ( + n n (d) 2 ) 1 ( + n n 14. The first term of an A.P. is 2 and common difference is 4. The sum of its 40 terms will be (a) 3200 (b) 1600 (c) 200 (d) 2800 15. If the sum of the series .. .......... 11 8 5 2 + + + is 60100, then the number of terms are (a) 100 (b) 200 (c) 150 (d) 250 16. The sum of all natural numbers between 1 and 100 which are multiples of 3 is (a) 1680 (b) 1683 (c) 1681 (d) 1682 17. The sum of ......... 7 5 3 1 + + + + upto n terms is (a) 2 ) 1 ( + n (b) 2 ) 2 ( n (c) 2 n (d) 2 ) 1 ( − n 18. If the sum of the series ... .......... 48 51 54 + + + is 513, then the number of terms are (a) 18 (b) 20 (c) 17 (d) None of these 19. If the sum of n terms of an A.P. is n n 5 2 2 + , then the th n term will be (a) 3 4 + n (b) 5 4 + n c) 6 4 + n (d) 7 4 + n 20. (The th n term of an A.P. is 1 3 − n .Choose from the following the sum of its first five terms (a) 14 (b) 35 (c) 80 (d) 40 21. If the first term of an A.P. be 10, last term is 50 and the sum of all the terms is 300, then the number of terms are (a) 5 (b) 8 (c) 10 (d) 15 22. The sum of the numbers between 100 and 1000 which is divisible by 9 will be (a) 55350 (b) 57228 (c) 97015 (d) 62140 23. The ratio of sum of m and n terms of an A.P. is 2 2 : n m , then the ratio of th m and th n term will be (a) 1 1 − − n m (b) 1 1 − − m n (c) 1 2 1 2 − − n m (d) 1 2 1 2 − − m n 24. The sum of the integers from 1 to 100 which are not divisible by 3 or 5 is (a) 2489 (b) 4735 (c) 2317 (d) 2632 25. The sum of the first and third term of an arithmetic progression is 12 and the product of first and second term is 24, then first te rm is (a) 1 (b) 8 (c) 4 (d) 6 26. The sum of numbers from 250 to 1000 which are divisible by 3 is (a) 135657 (b) 136557 (c) 161575 (d) 156375 27. th 7 term of an A.P. is 40, then the sum of first 13 terms is (a) 53 (b) 520 (c) 1040 (d) 2080 28. If sum of n terms of an A.P. is n n 5 3 2 + and 164 = m T then = m (a)26 (b) 27 (c) 28 (d) None of these 29. The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, the number of terms is (a) 10 (b) 11 (c) 12 (d) None of these 30. The number of terms of the A.P. 3,7,11,15...to be taken so that the sum is 406 is (a) 5 (b) 10 (c) 12 (d) 14 31. If the sum of the 10 terms of an A.P. is 4 times to the sum of its 5 terms, then the ratio of first term and common difference is (a ) 2 : 1 (b) 1 : 2 (c) 3 : 2 (d) 2 : 3 32. If 7 terms 10 to ......... 11 8 5 terms to .......... 7 5 3 = + + + + + + n , then the value of n is (a) 35 (b) 36 (c) 37 (d) 40 33. If the sides of a right angled triangle are in A.P., then the sides are proportional to (a) 1: 2: 3 (b) 2: 3: 4 (c) 3: 4: 5 (d) 4: 5: 6 34. If r q p r q p + + + 1 , 1 , 1 are in A.P., then (a) r q p , , , are in A.P. (b) 2 2 2 , , r q p are in A.P. (c) r q p 1 , 1 , 1 are in A.P. (d) None of these 35. If twice the 11 th term of an A.P. is equal to 7 times of its 21 st term, then its 25 th term is equal to (a) 24 (b) 120 (c) 0 (d) None of these