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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

$$S_{n}$$ = $$\frac{a_{1}(r^{n}-1) }{r-1}$$

where a₁ is the first term and r the common ratio

here a₁ = 0.5 and r = $$\frac{a_{2} }{a_{1} }$$ = $$\frac{1}{0.5}$$ = 2 , then

S₉ = $$\frac{0.5(2^{9}-1) }{2-1}$$

= $$\frac{0.5(512-1)}{1}$$

= 0.5(511)

= 255.5
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