
arithmetic progression
I need to find first term and common difference for an arithmetic progression where Un denotes the nth term and the sum of the first n terms is denoted Sn.
I am told U5 + U16 = 44 and that S18=3*S10
I cant see a way to find either of them... any help please.

$\displaystyle U_5 + U_{16} = 44$ and that$\displaystyle S_{18}=3*S_{10}$
Okay, 1st fact to remember
An A.P. is of the form: $\displaystyle a+(k1)d$, where $\displaystyle k\geq1$
where $\displaystyle U_k=a+(k1)d$ and $\displaystyle S_k=\frac{k(a+a+(k1)d)}{2}$
so $\displaystyle U_5=a+4d$ and $\displaystyle U_{16}=a+15d$
and $\displaystyle U_5+U_{16}=44$
$\displaystyle 2a+19d=44....(1)$
$\displaystyle S_{18}=\frac{18(a+a+17d)}{2}$
$\displaystyle S_{10}=\frac{10(a+a+9d)}{2}$
$\displaystyle S_{18}=3*S_{10}$
$\displaystyle \frac{18(a+a+17d)}{2}=3(\frac{10(a+a+9d)}{2})....( 2)$
Solve equations (1) and (2) simultaneously to obtain your answer.
