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Anit [1.1K]
3 years ago
13

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

Mathematics
1 answer:
Nuetrik [128]3 years ago
8 0

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.

as

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

g_1=-5

r=5

so

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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The prism is completely filled with 1750 cubes that have edge length of 15 ft.
neonofarm [45]

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Solution:

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<u>To find the volume of each cube:</u>

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                                    $=\left(\frac{1}{5} \right)^3

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<u>To find the volume of the prism:</u>

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7 0
3 years ago
benjamin is 4 years younger the kevan william is 4 years less than twice benjamins age if willian is 22 how old are kevan and be
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Kevin would be 14 and Benjamin would be 10
7 0
2 years ago
SIMPLIFY the expression! Please!
Levart [38]

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2 years ago
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Answer:

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Step-by-step explanation:

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