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Find the sum of the first 9 terms
of the geometric sequence: 0.5, 1, 2,-..

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S₉ = 255.5

Step-by-step explanation:

the sum to n terms of a geometric sequence is

[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 0.5 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{1}{0.5}[/tex] = 2 , then

S₉ = [tex]\frac{0.5(2^{9}-1) }{2-1}[/tex]

= [tex]\frac{0.5(512-1)}{1}[/tex]

= 0.5(511)

= 255.5
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