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goldfiish [28.3K]

2 years ago

8

Whats the rate of change

1 answer:

QveST [7]2 years ago

8 0

The line needs to start at the 0 it can’t be off the 0

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Write the first three terms of the series for which tn = 2(n+3). Find the number of terms of the series required to make the sum

ira [324]

Answer:

The first three terms of the series are 8, 10 and 12. The number of terms is 12 to make the sum 228.

Step-by-step explanation:

The series is defined as

$t_n=2(n+3)$

Put n=1.

$t_1=2(1+3)=2\times 4=8$

Put n=2.

$t_2=2(2+3)=2\times 5=10$

Put n=3.

$t_3=2(3+3)=2\times 6=12$

The first three terms of the series are 8, 10 and 12.

It is an arithmetic series. The first terms is 8 and the common difference is

$d=a_2-a_1=10-8=2$

The sum of n terms of an arithmetic series is

$S_n=\frac{n}{2}[2a+(n-1)d]$

$288=\frac{n}{2}[2(8)+(n-1)2]$

$288=\frac{2n}{2}[8+n-1]$

$288=n[n+7]$

$0=n^2+7n-288$

$0=n^2+19n-12n-288$

$0=n(n+19)-12(n+19)$

$0=(n+19)(n-12)$

Equate each factor equal to zero.

$n=-19,12$

The number of terms can not be negative, therefore the value of n must be 12.

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3 years ago

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Galina-37 [17]

Answer: see attachment

Step-by-step explanation:

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2 years ago

Which of the following is the solution to the differential equation....

bixtya [17]

Answer:

B

Step-by-step explanation:

$\frac{dy}{dx}= (x-2)(y-2)\\ y>2\\\frac{dy}{y-2}=(x-2)dx\\$

integrate both side

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3 years ago

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alukav5142 [94]

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Is 4.47 a rational number

zimovet [89]

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