SAMACHEER KALVI CLASS 10 - ASSIGNMENT 2 - SEQUENCE AND SERIES

 SAMACHEER KALVI

CLASS 10

SEQUENCE AND SERIES

ASSIGNMENT 2


1. Find all positive integers which when divided by 3 leaves remainder 2.


2. Prove that the product of two consecutive positive integers is divisible by 2.


3. Use Euclid's Division Algorithm to find the Highest Common Factor of 340 and 412.


4. If d is the HCF of 32 and 60, find x and y satisfying d = 32 x 
+ 60 y.


5. Find the HCF of 252525 and 363636.


6. If 13824  =  2^a  x  3 ^ b,  then find a and b.


7. Find the greatest numbers consisting of 6 digits which is exactly divisible by 24, 15 and 36?


8. Find the least positive value of x such that (i) 89 = (x+3) mod 4 (ii) 96 = (x/7 ) mod 5.


9. If x is congruent to 13 modulo 17 then 7x - 3 is congruent to which number modulo 17?


10. Solve 3x -2  = 0 ( mod 11 )


11. Find the remainder when 2⁸¹ is divided by 17?


12. Find the next three terms of the sequence 1/4, 2/9, 3/16,.....


13. Find the first four terms of the sequence whose nth term is given by n³ - 2.


14. Find the nth term of the sequence 2, 5, 10, .....


15. Check whether a-3, a-5, a-7 form an A.P.?


16. Given a=7, d=-5, find the corresponding A.P.


17. Find the 19th term of an A.P. : -11, -15, -19,.....


18. Find the middle term(s) of an A.P. 9, 15, 21, 27,.....183.


19. If nine times ninth term is equal to fifteen times fifteenth term, show that six times twenty fourth term is zero.


20. Find x, y and z given that the numbers x, 10, y, 24, z are in A.P.


21. The sum of three consecutive terms that are in A.P. is 27 and their product is 288. Find the three terms.


22. Find the sum of 3, 7, 11, .....  upto 40 terms.


23. Find the sum : 6 + 13 + 20 + .....+ 97.


24. Find the sum of first 28 terms of an A.P. whose nth term is 4n - 3.


25. Find the sum of all odd positive integers less than 450.


26. Are 120, 60, 30, 18, ..... in G.P.?


27. Find x so that x+6, x+12 and x+15 are in G.P.


28. Find the number of terms in the G.P. 4, 8, 16, .....8192.


29. In a G.P., the 9th term is 32805 and 6th term is 1215.  Find the 12th term.


30. Find the 10th term of a G.P. whose 8th term is 768 and the common ratio is 2.


31. Find the sum of first n terms of the G.P. 256, 64, 16, ......


32. Find the first term of the G.P. whose common ratio is 5 and whose sum to first 6 terms is 46872.


33. Find the sum to infinity of 9 + 3 + 1 + .....


34. Find the sum of the series 3 + 6 + 9 + .....+ 96.


35. Find the sum of the series 6²  +  7²  +  8²  + ..... + 21² .


36. The sum of the squares of the first n natural numbers is 285, while the sum of their cubes is 2025.  Find the value of n.




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