March 2021
BARC Quiz 2: Progressions
Arithmetic Progression, Harmonic Progression, Geometric Progression, Infinite Geometric Progression, Arithmetic Average, Harmonic Average, Geometric Average, Other forms of sequence or progression.
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Harmonic Progressions, HP
$h_n = \dfrac{n}{a_1 + (n - 1)d}$
Infinite Geometric Progression, IGP
$S = \dfrac{a_1}{1 - r}$
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Geometric Progression
Formulas:
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Arithmetic Progression
Formulas:
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There were 150 mg of a radioactive material stored at the start of the year 2000. The material has a half-life of 15 years. How much radioactive material will there be at the start of 2040?
There were 150 mg of a radioactive material stored at the start of the year 2000. The material has a half-life of 15 years. How much radioactive material will there be at the start of 2040?
Solve for x from $7^{2x - 1} = 3^{x + 1}$.
Solve for x from $7^{2x - 1} = 3^{x + 1}$.
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Given $\log_a 2 = x$, $\log_a 5 = y$, and $\log_a 6 = z$, express $\log_a 0.15$ in terms of x, y, and z.
Given $\log_a 2 = x$, $\log_a 5 = y$, and $\log_a 6 = z$, express $\log_a 0.15$ in terms of x, y, and z.
The middle term in the expansion of $(x^3 + 4)^{10}$ is...
The middle term in the expansion of $(x^3 + 4)^{10}$ is...
$\log_3 11 = x$. What is the value of x?
$\log_3 11 = x$. What is the value of x?
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