Home

Solve any problem
(step by step solutions)
Input table (Matrix, Statistics)
Mode :
SolutionHelp
Solution
Problem: If S1, S2, S3 are sum of n, 2n, 3n terms of arithmetic progression series then prove that S3 = 3(S2 - S1) [ Calculator, Method and examples ]

Solution:
Your problem `->` If S1, S2, S3 are sum of n, 2n, 3n terms of arithmetic progression series then prove that S3 = 3(S2 - S1)


Let a be the first term and d be the common difference
Now,
`S_1= n/2 [ 2a + (n - 1) d ]`

`S_2 = (2n)/2 [ 2a + (2n - 1) d ]`

`S_3 = (3n)/2 [ 2a + (3n - 1) d ]`


Now, `3(S_2 - S_1)`

`= 3 [ (2n)/2 ( 2a + (2n - 1) d ) - n/2 ( 2a + (n - 1) d ) ]`

`= 3 [ n/2 ( 2(2a) - 2a ) + n/2 ( 2(2n - 1) d - (n - 1) d ) ]`

`= 3 [ n/2 ( 2a ) + n/2 ( 4n - 2 - n + 1) d ) ]`

`= 3 [ n/2 ( 2a ) + n/2 ( 3n - 1) d ) ]`

`= (3n)/2 [ 2a + ( 3n - 1) d ]`

`= S_3` (Proved)






Solution provided by AtoZmath.com
Any wrong solution, solution improvement, feedback then Submit Here
Want to know about AtoZmath.com and me
  
 

 
Copyright © 2019. All rights reserved. Terms, Privacy





We use cookies to improve your experience on our site and to show you relevant advertising. By browsing this website, you agree to our use of cookies. Learn more