3 years ago

Which choice is the explicit formula for the following geometric sequence?0.5, -0.1, 0.02, -0.004, 0.0008, ...

1 answer:

8 0

$a_1=0.5\\a_2=-0.1\\a_3=0.02\\a_4=-0.004\\a_5=0.0008\\\\a_n=a_1\cdot q^{n-1}\\\\q=a_2:a_1\to q=-0.1:0.5=-0.2\\\\a_n=0.5\cdot(-0.2)^{n-1}=0.5\cdot(-0,2)^n\cdot(-0.2)^{-1}\\\\=0.5\cdot(-0.2)^n\cdot(-5)=-2.5\cdot(-0.2)^n\\\\\boxed{a_n=-2.5\cdot(-0.2)^n}$

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Step-by-step explanation:

It was given that the points $(-3,4)$ and $(5,-2)$ are on the graph of the function $f$ .

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Hence we will have the ordered pairs $(4,-3)$ and $(-2,5)$

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In other words, f and g are symmetric about the line $y=x$ . This implies that when we reflect the points $(-3,4)$ and $(5,-2)$ in the line $y=x$ we will obtain $(4,-3)$ and $(-2,5)$ .