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2 years ago

Four students are competing in a race. In how many different combinations could the four students place in the race?

1 answer:

4 0

"Combinations" isn't really the right word, because a combination doesn't take order of elements into account, and the outcome of a race certainly does depend on order. "Permutations" would be the correct term.

If 4 students are competing, then the race has

4! = 4 • 3 • 2 • 1 = 24

possible outcomes.

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3 years ago

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3 years ago

Mohamed and Li Jing were asked to find an explicit formula for the sequence -5, -25, -125, -625,....

Nuetrik [128]

Answer:

Li Jing's formula i.e. $\boxed{g_n=-5\cdot \:5^{n-1}}$ is right.

Step-by-step explanation:

Considering the sequence

$-5,\:-25,\:-125,\:-625,...$

A geometric sequence has a constant ratio r and is defined by

$g_n=g_0\cdot r^{n-1}$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{g_{n+1}}{g_n}$

$\frac{-25}{-5}=5,\:\quad \frac{-125}{-25}=5,\:\quad \frac{-625}{-125}=5$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$r=5$

So, the sequence is geometric.

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$g_1=-5$

$r=5$

$g_n=g_1\cdot r^{n-1}$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$g_n=-5\cdot \:5^{n-1}$

Therefore, Li Jing's formula i.e. $\boxed{g_n=-5\cdot \:5^{n-1}}$ is right.

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3 years ago

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