Hey, so i am confused about this question
1. The common difference of an artimemetic sequence is 4. Show
that :
ÖS_{2n}-2S_{n} =2n
The funny O is a square root sign that extends untill the equals sign.
Can somebody please help me !!
Hey, so i am confused about this question
1. The common difference of an artimemetic sequence is 4. Show
that :
ÖS_{2n}-2S_{n} =2n
The funny O is a square root sign that extends untill the equals sign.
Can somebody please help me !!
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
$\displaystyle \begin{cases}S_n=\frac{n}{2}(2a_1+(n-1)d) \\S_{2n}=n(2a_1+(2n-1)d) \end{cases}$
therefore :
$\displaystyle \begin{cases}S_n=n(a_1+2(n-1)) \\S_{2n}=2n(a_1+2(2n-1)) \end{cases}$
hence :
$\displaystyle \sqrt{2n(a_1+2(2n-1))-2n(a_1+2(n-1))}=2n$
$\displaystyle \sqrt{4n(2n-1)-4n(n-1)}=2n$
$\displaystyle \sqrt{4n(2n-1-n+1)}=2n$
$\displaystyle \sqrt{4n^2}=2n$
$\displaystyle 2n=2n$