Arithmetic Mean

Important

Arithmetic mean

  • Arithmetic Mean = $$ \dfrac{x_{1}+x_{2}+x_{3}…x_{n}}{n}$$

  • The arithmetic mean = $$\frac{Sum  of  all  the  terms}{Number  of  terms}$$
  • If two numbers A and B are in A.P then arithmetic mean= $$\frac{a+b}{2}$$
  • Inserting 'n' means between two numbers a and b.
  • The total terms will become n+2, a is the first term and b is the last term
  • Then the common difference d= $$\frac{b-a}{n+1}$$
  • The last term b=a+(n+1)d
  • The final series is a, a+d, a+2d,....
Question 1

The sum of the first and tenth numbers of an arithmetic progression is 80. What is the average of the 5th and 6th terms of the arithmetic progression?

Question 2

S = {1,2,3,4, . . . , 2n) where n > 20. X is the average of the odd integers in S and Y is the average of even integers in S. The value of X-Y is

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Arithmetic Mean

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A.P. - Formulas and Properties

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