Xi Sequence And Series Assignment

ASSIGNMENT CLASS XI SEQUENCE AND SERIES 1. If m time the mth term of an A.P is equal to the n times the nth term, then show that the (m  n)th term of the A.P. is zero. 2. Which term of the A.P. 121, 117, 113, … is the first negative term? 3. How many three digit numbers leave the remainder 2 when divided by 9? 4. Find three numbers in A.P. whose sum is 21 and sum of whose squares is 155. 5. How many terms of the A.P. 54, 51, 48, … are needed to give the sum 513? Explain the double answer. n ( a  b) 6. Prove that the sum of n arithemetic means between a and b is . 2 7. (a)There are n arithemetic means between 1 and 23 such that the ratio of the last mean to the first mean is 7:1. Find the value of n . (b) Between 7 and 85 are inserted m arithmetic means so that the ratio of (m – 3)th and mth means is 11:24. Find the value of m. 8. If a , b , c are in the A.P., prove that the following are also in A.P.: 1 1 1 1 1 1 (i ) b  c, c  a, a  b (ii ) , , (iii ) , , bc ac ab b c c a a b 9. If the fourth and the ninth terms of a G.P. are 54 and 13122 respectively, find the sixth term of the G.P. 10. If a , b , c , d are in G.P., prove that the following are also in G.P.:

(i ) a  b, b  c, c  d (ii ) a 2  b 2 , b 2  c 2 , c 2  d 2 (iii ) a n  b n , b n  c n , c n  d n 11. Find three numbers in G.P. whose sum is 7 and product is 8. 12. The sum of three numbers in A.P. is 21. If 2nd is reduced by 1 and 3rd is increased by 1, numbers forms a G.P. Find the numbers. 13. How many terms of the series 2 + 6 + 18 + … must be taken to make the sum 728? 15

14. Evaluate the following:

(i )  (1  3k 1 ) k 2

k 1 k 1 10  1 1  (ii )         5   k 1   2 

15. (a)Find two numbers whose A.M. is 34 and G.M. is 16. (b) Find two positive numbers whose difference is 12 and whose A.M. exceeds the G.M. by 2. 16. Prove that the product of n G.M.’s between two numbers a and b is





n

ab .

17. Find the sum of n terms of the series whose nth terms are given by: (i ) n(n  1) (ii ) n 2  3n  1 (iii ) n 2  3n (iv ) n3  2n 18. Find the sum of the following series up to n terms: (i )12  32  52  ... (ii )1  (1  2)  (1  2  3)  ... (iii )1.2.5  2.3.6  3.4.7  ... (iv ) 6 13  24  39  ... (v) 2  5  10  17  ... (vi) 3  7 14  24  37  ... ANSWERS 2. 32nd 3. 100

4. 5, 7, 9 or 9, 7, 5

5. 18, 19 7. (a)10 (b) 5 9. 486 11. 1, 2, 4 or 4, 2, 1 15 25  3 1 12. 3, 7, 11 or 12, 7, 2 13. 6 14. (i ) (ii ) 2(1  210 )  (1  510 ) 2 20 1 1 1 3 15.(a) 4, 64 (b) 16 , 4 17. (i ) n(n  1)(n  2) (ii ) n(n  2)(n  4) (iii ) n(n  1)(2n  1)  (3n  1) 3 3 6 2 1 1 1 1 (iv ) n(n  1)(n 2  n  4) 18. (i ) n(4n 2 1) (ii ) n(n  1)(n  2) (iii ) n(n  1)(n  2)(3n  17) 4 3 6 12 1 1 1 (iv ) n(4n 2  9n  23) (v) n(2n 2  3n  7) (vi) n(n 2  n  4) 6 6 2

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