Prove the arithmetic progressions equation, Mathematics

Assignment Help:

Prove that am + n + am - n  =2am

Ans:    a m + n = a1 + (m + n - 1) d

a m-n = a1 + (m - n -1) d

am = a1 + (m-1) d

Add 1 & 2

a m+n + a m-n  =   a1+(m+n-1) d+ a1 + (m-n-1)d

=          2a1+(m+n+m-n-1-1)d

=          2a1+ 2(m-1)d

=          2[a1+ (m-1)d]

=          2[a1+ (m-1)d]

=          2am.       Hence proved.


Related Discussions:- Prove the arithmetic progressions equation

What are the basic elements of reasoning, What are the Basic Elements of Re...

What are the Basic Elements of Reasoning ? There are four basic elements used in geometry. If we say studying geometry is like building a house, then these elements are like d

Estimate percent of the babies born among 6 and 8.5 pounds, 25% of babies b...

25% of babies born at Yale New Haven Hospital weigh less than 6 pounds and 78% weigh less than 8.5 pounds. What percent of the babies born at Yale New Haven Hospital weigh among 6

Probability transition matrices or brand switching, Define the Probability ...

Define the Probability Transition Matrices or Brand switching.

How to find total no. of unordered pairs , How to find total no. of unorder...

How to find total no. of unordered pairs of disjoint subsets of a finite set? Solution) Suppose A and B are two such disjoint subsets of the set S. Then every element can go into

Subtraction involving negative numbers, Q. Subtraction Involving Negative N...

Q. Subtraction Involving Negative Numbers? In order to subtract positive and negative numbers, you need to be aware of the Rule for Subtraction. This rule states that subtracti

Evaluate the mean of temperatures, Evaluate the mean of temperatures: ...

Evaluate the mean of temperatures: Example: Given the subsequent temperature readings, 573, 573, 574, 574, 574, 574, 575, 575, 575, 575, 575, 576, 576, 576, 578 So

How i get orders, how i become an assignment helper?n how i get order from ...

how i become an assignment helper?n how i get order from students?what should i do

Explain mixed numbers with examples, Explain Mixed Numbers with examples? ...

Explain Mixed Numbers with examples? Everybody loves a bargain, right? But sometimes these "special deals" aren't what they seem to be. For example, pretend you were at a

System of linear equations, create a system of linear equations that has (2...

create a system of linear equations that has (2,3)as a solution.

Example of imaginary numbers, Example of Imaginary Numbers: Example 1...

Example of Imaginary Numbers: Example 1: Multiply √-2  and √-32 Solution: (√-2)( √-32) = (√2i)( √32i) =√64 (-1) =8 (-1) =-8 Example 2: Divid

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