How do you find the first five terms of the geometric sequence $a_{1} = 576$ $a_1=576$ , r=-1/2?

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Answer 1 · 2016-12-13T11:46:18

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$a_{1} = 576 {(- \frac{1}{2})}^{0} = 576 \times (1) = + 576$ $a_1=576(-1/2)^0 = 576xx(1) =+576$

$a_{2} = 576 {(- \frac{1}{2})}^{1} = - 288$ $a_2=576(-1/2)^1=-288$

$a_{3} = 576 {(- \frac{1}{2})}^{2} = + 144$ $a_3=576(-1/2)^2 = +144$

$a_{4} = 576 {(- \frac{1}{2})}^{3} = - 72$ $a_4=576(-1/2)^3 = -72$

$a_{5} = 576 {(- \frac{1}{2})}^{4} = + 36$ $a_5=576(-1/2)^4= +36$

By observation, for any $i$ $i$ we have $a_{i} = 576 {(- \frac{1}{2})}^{i - 1}$ $a_i=576(-1/2)^(i-1)$

How do you find the first five terms of the geometric sequence a_1=576a1=576a_1=576, r=-1/2?