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SERIES question (1 Viewer)

Thread starter hollaholla
Start date Jun 4, 2009

H

hollaholla

Member

#1

can anyone do this for me?

A geometric series has a limiting sum of 9 and second term 2 . Find the values of a and r?

thank you.

gurmies

Drover

#2

$S_{\infty }=\frac{a}{1-r}=9 \\\\ T_{n}=ar^{n-1} \\\\ T_{2}=ar=2 \\\\ a=\frac{2}{r} \\\\\frac{2}{r(1-r)}=9 \\\\ 9r-9r^{2}=2 \\\\ 9r^{2}-9r+2=0 \\\\ (3r-1)(3r-2)=0, \,\, r=\frac{1}{3} \,\, or/ \,\, r=\frac{2}{3} \\\\ When\,\,r=\frac{1}{3}, \,\, a=6 \\\\When \,\,r=\frac{2}{3}, \,\,a=3$

H

hollaholla

Member

#3

i thank you.

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