Arithmetic mean, Mathematics

Assignment Help:

When three quantities are in A.P., then the middle one is said to be the arithmetic  mean of the other two. That is, if a, b and c are in A.P., then b is the arithmetic mean of a and c. Since a, b and c are in A.P., the common difference ought to be constant, we have

b - a

= c - b

 or   b + b 

= a + c

or      2b

= a + c

or      b

= (a+c)/2

We should remember that between any two quantities we can insert any number of terms so that the resultant series is in A.P. Now we look at some examples wherein we will insert the required number of terms.

Example 

Insert 15 arithmetic means between 4 and 68.

We are given the first term and the last term. The total number of terms including 4 and 68 are therefore 17. Since "a" is given we ought to find "d". The 17th term is given by T17 = a + 16d = 4 + 16d. Also the T17 term is given to be 68. Therefore,

68 = 4 + 16d
16d = 68 - 4
16d = 64

d

= 64/16 = 4

Using the values of "a" and "d" we insert the required terms. The series will be 4, 8, 12, ..., 68.   


Related Discussions:- Arithmetic mean

Pythagorean theorem, when one side of a triangle is 15cm and the bottom of ...

when one side of a triangle is 15cm and the bottom of the triangle is 12cm what would x be rounded to the nearest tenth?

Pigeonhole principle, By pigeonhole principle, show that if any five number...

By pigeonhole principle, show that if any five numbers from 1 to 8 are chosen, then two of them will add upto 9.    Answer: Let make four groups of two numbers from 1 to 8 like

Find the equation to the pair of lines - coordinate geometry, 1. Find the n...

1. Find the number of zeroes of the polynomial y = f(x) whose graph is given in figure. 2 Find the circumcentre of the triangle whose vertices are (-2, -3), (-1, 0) and (7,-6).

Differential equations, Find the normalized differential equation which has...

Find the normalized differential equation which has {x, xex} as its fundamental set

What is plotting points, What is Plotting Points? To "plot" or "graph" ...

What is Plotting Points? To "plot" or "graph" values means to find points on a number line. The numbers four, negative two, negative three, zero, two, and negative four are bei

Definition of the definite integral , Using the definition of the definite ...

Using the definition of the definite integral calculate the following.                                                             ∫ 0 2  x 2   + 1dx Solution Firstly,

Draw a common graph f ( x ) = |x|, Graph f ( x ) = |x| Solution The...

Graph f ( x ) = |x| Solution There actually isn't much to in this problem outside of reminding ourselves of what absolute value is. Remember again that the absolute value f

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd