2 years ago

Yasmine bought 4 bracelet. Each bracelet cost $ 3

Mathematics

1 answer:

Morgarella [4.7K]2 years ago

5 0

She spent a total of $12

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2 years ago

The 13th term of a geometric sequence is 16, 384 and the first term is 4. What is the common ratio?

AleksAgata [21]

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$\large \boxed{2}$

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The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

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$\begin{array}{rcl}16384 & = & 4r^{(13 - 1)}}\\16384 & = & 4r^{12}\\4096 & = & r^{12}\\3.6124 & = & 12 \log r\\0.30102 & = & \log r\\r & = & 10^{0.30102}\\ & = & \mathbf{2}\\\end{array}\\\text{The common ratio is $\large \boxed{\mathbf{2}}$}$

Check:

$\begin{array}{rcl}16384 & = & 4(2)^{12}\\16384 & = & 4(4096)\\16384 & = & 16384\\\end{array}$

It checks.

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Factor the expression 2^2 +4-12

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