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2 years ago

Write an explicit equation for the following sequence. 100, 97, 94, 91, ...

Mathematics

1 answer:

pishuonlain [190]2 years ago

6 0

Answer:

$a_{n}$ = 103 - 3n

Step-by-step explanation:

there is a common difference between consecutive terms , that is

97 - 100 = 94 - 97 = 91 - 94 = - 3

This indicates the sequence is arithmetic with explicit equation

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 100 and d = - 3 , then

$a_{n}$ = 100 - 3(n - 1) = 100 - 3n + 3 = 103 - 3n

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Standard deviation

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For 1st: |1720-1593|^2=8836

For 2nd: |1687-1593|^2=10201

For 3rd: |1367-1593|^2=51076

For 4th: |1614-1593|^2=441

For 5th: |1460-1593|^2=1689

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S.D = sqrt((summation of |x-m|^2) / n-1)

S.D=sqrt(171968/6)

S.D=sqrt(28661.33)

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Standard deviation is 169.30

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3 years ago

<img src="https://tex.z-dn.net/?f=15%20x%5E%7B2%7D%20%2B14x-49%3D0" id="TexFormula1" title="15 x^{2} +14x-49=0" alt="15 x^{2} +1

Alex777 [14]

$15x^2+14x-49=0\\\\
Terms:\\
a=15\ \ \ \ b=14\ \ \ \ c=-49\\
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x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\
x=\dfrac{-14\pm\sqrt{196+2,940}}{30}\\\\
x=\dfrac{-14\pm\sqrt{3,136}}{30}\\\\
x=\dfrac{-14\pm56}{30}$

$Roots:\\\\
x'=\dfrac{-14+56}{30}\\\\
x'=\dfrac{42}{30}\\\\
x'=\dfrac{21}{15}\\\\
\boxed{x'=\dfrac{7}{5}}\\\\\\\\
x''=\dfrac{-14-56}{30}\\\\
x''=\dfrac{-70}{30}\\\\
\boxed{x''=\dfrac{-7}{3}}$

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