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 is combination formula, Q. What is Combination Formula? Ans. ...

Q. What is Combination Formula? Ans. The difference between combinations and permutations is that permutations take ordering into consideration, whereas combinations do no

Tangents, two circle of radius of 2cm &3cm &diameter of 8cm dram common tan...

two circle of radius of 2cm &3cm &diameter of 8cm dram common tangent

Define a complete lattice, Define a complete lattice and give one example. ...

Define a complete lattice and give one example. Ans:  A lattice (L, ≤) is said to be a complete lattice if, and only if every non-empty subset S of L has a greatest lower bound

Arithmetic/geometric sequences and binomial expansion, find s10 for the ari...

find s10 for the arithmetic sequenxe inwhich a1=5 and a10=68

Heat loss in a cylindrical pipe, which laws of physics are used to discuss ...

which laws of physics are used to discuss heat loss in a pipe

Algebra, Multiple response question.Zack puts a mug of water ni his microwa...

Multiple response question.Zack puts a mug of water ni his microwave oven. He knows that the final temperature of the water will be a function of the number of seconds he heats the

Describe common phrases to represent math operations, Describe Common Phras...

Describe Common Phrases to Represent Math Operations? The table below shows the common phrases used in word problems to represent addition, subtraction, multiplication, and div

Find out a particular solution to equation, Example: Find out a particular...

Example: Find out a particular solution to y'' - 4y' - 12 y = 3e 5t Solution The point here is to get a particular solution, though the first thing that we're going to

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