1. ## Sequences and Series

Show that 28, 23, 18, 13....... is arithmetic and hence find un and the sum of sn of the first n terms in simplest form.

I got un=23+5n and sn=n/2(51+5n)
but the answers in the book are:
un=33-5n and sn=n/2(61-5n)
so i dont know where I went wrong

2. Hello, juliak!

Show that $28, 23, 18, 13, \hdots$ is arithmetic
and hence find $u_n$ and the sum $S_n$ of the first $n$ terms.

The first term is: . $u_1 = 28$

The common difference is: . $d = -5$

The $n^{th}$ term is: . $u_n \:=\:u_1 + (n-1)d$

So we have: . $u_n \:=\:28 + (n-1)(-5)\quad\Rightarrow\quad\boxed{ u_n \:=\:33-5n}$

The sum of the first n terms is: . $S_n \;=\;\frac{n}{2}\bigg[2u_1 + (n-1)d\bigg]$

So we have: . $S_n \;=\;\frac{n}{2}\bigg[2(28) + (n-1)(-5)\bigg] \quad\Rightarrow\quad\boxed{ S_n \;=\;\frac{n}{2}(61-5n)}$