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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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yawa3891 [41]
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In order to find r you have to find the distance between C(-2, 1) and let's say A(-4, 1)

The formula for distance is:
\sqrt{  ( y_{A}-y_{C )^{2} + (x_{A}- x_{C )^{2} }
r = 2

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I hope that this is the answer that you were looking for and it has helped you.

5 0
3 years ago
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3241004551 [841]

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Because it's estimation. So, we need to estimate the number 7872 to 8000.

In order to divide 8000 by a number we need to estimate 305 to the 400. Because 400 is exact divisor of 8000.

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6 0
3 years ago
Please find the area of the square I forgot how to do this please help :(
Strike441 [17]

Answer:

85/2 or 42.5 ft²

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4 0
3 years ago
Read 2 more answers
The YMCA lap pool is a right rectangular prism 36.8\, \text{m}36.8m36, point, 8, start text, m, end text long by 20 \,\text{m}20
PilotLPTM [1.2K]

Volume is a three-dimensional scalar quantity. The depth of the YMCA lap pool is 2 meters.

<h3>What is volume?</h3>

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given that the following details about the YMCA lap pool:

  • The volume of the pool = 1472m³
  • The length of the pool = 36.8m
  • The width of the pool = 20 m

Since the pool is in the space of a right rectangular prism, therefore, the volume of the prism will be the product of length, width and depth. Therefore, the volume of the pool can be written as,

The volume of the pool = Length × width × depth

1472m³ = 36.8m × 20 m × depth of the pool

Depth of the pool = (1472m³ ) / (36.8m × 20m)

                              = 2 meter

Hence, the depth of the YMCA lap pool is 2 meters.

Learn more about Volume here:

brainly.com/question/13338592

#SPJ1

3 0
1 year ago
Estimate the sum of the decimal below by rounding to the nearest whole number.
Marizza181 [45]
The non-rounded sum is 15.579, so you’d round up to 16 since 5 and up rounds up. Hope this helps<3
4 0
3 years ago
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