# Arithemetic Sequence question !!

• March 13th 2013, 03:12 AM
AzraaBux
Arithemetic Sequence question !!

1. The common difference of an artimemetic sequence is 4. Show
that :

ÖS2n-2Sn =2n

The funny O is a square root sign that extends untill the equals sign.

• March 13th 2013, 04:25 AM
MINOANMAN
Re: Arithemetic Sequence question !!
AzraaBux

revise the chapter of the arithmetic sequences and find the formula that gives the sum of n terms of an arithmetic sequence
apply this formula twice ..
once for 2n terms and second time for n terms. then subtract the two expressions and your answer will come very easily.

dont forget that the 2nth term of the arithmetic sequence is a-(2n-1)4 while the nth term is a+(n-1)4 . a represents the first term of the sequence but it will cancel with the subtraction.
I did it my self and it is easy...try it.
MINOAS
• March 13th 2013, 05:35 AM
princeps
Re: Arithemetic Sequence question !!
$\begin{cases}S_n=\frac{n}{2}(2a_1+(n-1)d) \\S_{2n}=n(2a_1+(2n-1)d) \end{cases}$

therefore :

$\begin{cases}S_n=n(a_1+2(n-1)) \\S_{2n}=2n(a_1+2(2n-1)) \end{cases}$

hence :

$\sqrt{2n(a_1+2(2n-1))-2n(a_1+2(n-1))}=2n$

$\sqrt{4n(2n-1)-4n(n-1)}=2n$

$\sqrt{4n(2n-1-n+1)}=2n$

$\sqrt{4n^2}=2n$

$2n=2n$
• March 13th 2013, 05:38 AM
AzraaBux
Re: Arithemetic Sequence question !!
Thanks so much Cool Kidds :):) really appreaciate it :)
• March 13th 2013, 11:39 AM
MINOANMAN
Re: Arithemetic Sequence question !!
I believe we should guide the students accordingly to do their HW and solve their questions rather than solve the HW for them.
MINOAS