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3 years ago

The sum of the first n consecutive even numbers can be found using S = n2 + n. What is the value of n when the sum is 272?

Mathematics

2 answers:

Harman [31]3 years ago

8 0

Answer:

n>2

Step-by-step explanation:

The sum of the first n consecutive even numbers can be found using S = n2 + n, where n > 2.

Citrus2011 [14]3 years ago

6 0

Answer:

The sum of the first n consecutive even numbers can be found using

The sum of the first n consecutive even numbers can be found using S = n2 + n, where n >

Step-by-step explanation:

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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.

8 0

3 years ago

Manuel deposited $150 in his savings account on january 1. on the first day of each following month, he deposited an additional

posledela

Answer:

8 months

Step-by-step explanation:

Subtract $150 from $430 to get $280, the amount if money that Manuel has to earn to reach his goal.

If he is adding $35 to his account each month, then all you have to do is divide the amount you need by the amount you are earning each month to get the number of months until you reach your goal.

$280 divided by $35 is 8, so it would take 8 months for Manuel to reach his goal.

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3 years ago

How to do this problem??

ahrayia [7]

The answer would be 16 3/4 divided by 3 7/8

7 0

3 years ago

Help with the following problem please

Effectus [21]

Given:
The largest circle has a radius of R=7 units.
Let x be the radius of the large shaded circle.
The small shaded circles have a radius of 1/5 of the large shaded circle.
=> the small shaded circles have a radius of r=x/5

By adding up radii, we have the equation
2(r+x+r)=2(x/5+x+x/5)=2R=2*7=14
Simplify:
7x/5=14/2
x=5
=> r=1

Area of outer circle = $\pi R^2=\pi7^2=49\pi$
Area of large shaded circle = $\pi x^2=\pi5^2=25\pi$
Area of 4 small shaded circles = $4\pi r^2=4\pi1^2=4\pi$
Total area of shaded circles = $25\pi+4\pi=29\pi$

Shaded area as a fraction of that of the outer circle
$=\frac{29\pi}{49\pi}=29/49$

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kvasek [131]

Answer:

Step-by-step explanation:

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