series

**14041471** · May 31st 2009, 01:52 PM

"Find s_3 , the third term in the series which corresponds to the geometric sequence which has a = 8 and r = 1/4"

I'm not sure what the method is in order to work out what s_3 is..

**pberardi** · May 31st 2009, 02:15 PM

Originally Posted by 14041471

"Find s_3 , the third term in the series which corresponds to the geometric sequence which has a = 8 and r = 1/4"

I'm not sure what the method is in order to work out what s_3 is..

The formula for finding the nth Term of a Geometric Sequence is
a_n = a_1*r^(n-1)

I am going to just assume that you made a typo and that your a = 8 is really a_1 = 8. If not please disregard.

a_3 = 8*(1/4)^(2)
a_3 = 8*(1/16)
a_3 = 1/2

**pickslides** · May 31st 2009, 02:28 PM

$S_n = \frac{a(1-r^n)}{(1-r)}$

$S_3 = \frac{8(1-\frac{1}{4}^3)}{(1-\frac{1}{4})}$

$S_3 = \frac{21}{2}$

also $S_3 = a_1+a_2+a_3$

$S_3 = 8+2+\frac{1}{2}= \frac{21}{2}$

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