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ARITHMETIC PROGERESSIONS


 



  1. Find the sum of 20 terms of the A.P. 1,4,7,10………
  2. If the nth terms of an A.P is (2n + 1), find the sum of first n terms of the A.P.
  3. Find the sum of first 30 terms of an A.P.whose second term is 2 and seventh term is 22.
  4. Find the sum of first 10 terms of an A.P., in which 3rd term is 7 and 7th term is two more than thrice of its 3rd term.
  5. Find the sum of all even integers between 2 to 100 divisible by 2.
  6. Find the number of terms in the series 20, 19 1/3 + 18 2/3 +………of which the sum is 300,explain the double answer.
  7. If the mth term of an A.P. is 1/n and the nth terms is 1/m, show that the sum of mn terms is ½(nm + 1).
  8. If the sum of n terms of an A.P.is same as the sum of its n terms, show that the sum of its (m + n) terms is zero.
  9. Find the sum of first n odd natural numbers.
  10. If the 8th terms of an A.P.is 31 and the 15th terms is 16 more than the 11th terms find the sum of first 20 terms.
  11. How many terms of A.P.: 24,21,18,…….. Must be taken so that their sum is 78?
  12. The angles of a triangle are in AP.If the greatest angle equals the sum of the other two, find the angles.
  13. Find the sum of two digits numbers, which are divisible by 7?
  14. Find the sum of number b/t 49 to 500 which are divisible by 7?
  15. If the pth term of an A.P.is q and the qth term is p, prove that its nth term is (p + q – n) and find the sum of first (p+q)th term .
  16. How many terms of the sequence 18,16,14…… should be taken so that their sum is zero.
  17. Write the first 5 terms of an AP whose nth term is given by (2n+1)/3.
  18. How many terms in the sequence -6  , -11/2 , -5 , -9/2 , …are needed to give the sum 0 ?
  19. Find the sum of all the natural numbers less than 100 which are divisible by 6.
  20. The sum of n terms of an A.P.; be 3n2 – n and its common difference is 6,find its first and 27th term.
  21. The sum of nth terms of an A.P. is 3n2+ 5n, then find its nth term.
  22. Find the sum of first 21 terms Ö2 + Ö8 + Ö18 + Ö32………….

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