arithmetic progression

**cpj** · November 24th 2009, 03:37 PM

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.

**I-Think** · November 24th 2009, 06:09 PM

$U_5 + U_{16} = 44$ and that $S_{18}=3*S_{10}$

Okay, 1st fact to remember
An A.P. is of the form: $a+(k-1)d$ , where $k\geq1$
where $U_k=a+(k-1)d$ and $S_k=\frac{k(a+a+(k-1)d)}{2}$

so $U_5=a+4d$ and $U_{16}=a+15d$
and $U_5+U_{16}=44$
$2a+19d=44....(1)$

$S_{18}=\frac{18(a+a+17d)}{2}$
$S_{10}=\frac{10(a+a+9d)}{2}$

$S_{18}=3*S_{10}$
$\frac{18(a+a+17d)}{2}=3(\frac{10(a+a+9d)}{2})....( 2)$

Solve equations (1) and (2) simultaneously to obtain your answer.

**cpj** · November 24th 2009, 07:27 PM

Thanks!!

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