Arithmetic Mean Assignment Help

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Arithmetic Mean:

  • If three terms are in A.P., then the middle term is known as the arithmetic mean (A.M.) between the other two i.e. if a,b,c are in A.P. then b=a+c/2 is the A.M. of a and c.
  • If a1, a2, ...an are n numbers then the arithmetic mean (A) of these numbers is  529_Arithmetic Mean.png
  • The n numbers A1, A2......An are said to be A.M's between the numbers b and a if a, A1, A2,........An,b are in A.P. If d is the common difference of that A.P. then
    1237_Arithmetic Mean1.png.

 

Problem: If the Ist and the 2nd terms of an A.P are 1 and -3 respectively, calculate the nth term and the addition of the Ist n terms.

Solution: Ist term = a, 2nd term = a + d where a = 1, a + d = -3,

                              Þ d = -4 (Common difference of A.P.)

                               we have an = a + (n -1)d

                              = 1 + (n - 1) (-4) = 5 - 4n

                            1430_Arithmetic Mean2.png

 

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