"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..
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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
$\displaystyle S_n = \frac{a(1-r^n)}{(1-r)}$ $\displaystyle S_3 = \frac{8(1-\frac{1}{4}^3)}{(1-\frac{1}{4})}$ $\displaystyle S_3 = \frac{21}{2}$ also $\displaystyle S_3 = a_1+a_2+a_3$ $\displaystyle S_3 = 8+2+\frac{1}{2}= \frac{21}{2}$
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