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ikadub [295]
3 years ago
11

Write a sequence that has four geometric means between 31 and –23,540,625.

Mathematics
2 answers:
tino4ka555 [31]3 years ago
7 0

Answer:

a_n=31(-15)^{n-1}

31, -465, 6975, -104,625, 1,569,375, -23,540,625

Step-by-step explanation:

The formula for a geometric sequence is:

a_n=a_1(r)^{n-1}

The formula for a geometric sequence is:

Where

r is the common ratio

a_1 is the first term

a_n is the nth term

In this case

a_1=31

a_6=-23,540,625

So:

-23,540,625=31(r)^{6-1}

Now we solve for r

-23,540,625=31(r)^{5}

-\frac{23,540,625}{31}=r^{5}\\\\r=\sqrt[5]{-\frac{23,540,625}{31}}\\\\r=-15

Then the four geometric means are

a_2=31(-15)^{2-1}=-465

a_3=31(-15)^{3-1}=6975

a_4=31(-15)^{4-1}=-104,625

a_5=31(-15)^{5-1}=1,569,375

31, -465, 6975, -104,625, 1,569,375, -23,540,625

aleksandr82 [10.1K]3 years ago
7 0

Answer:

31, -465, 6975, -104,625, 1,569,375, -23,540,625

Step-by-step explanation:

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Amelia must substitute 8 for the variable using parentheses. To simplify, Amelia must multiply 8 by 6. 8 is not a solution of the equation.

<h3>What is algebraic expression?</h3>

Algebraic expression are the expression which consist the variables, coefficients of variables and constants.

The algebraic expression are used represent the general problem in the mathematical way to solve them.

Amelia is using substitution to determine if 8 is a solution to the equation.  The equation which is Amelia is solving  for a = 8 is,

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First, Amelia must substitute 8 for the variable using parentheses as,

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Thus, Amelia must substitute 8 for the variable using parentheses. To simplify, Amelia must multiply 8 by 6. 8 is not a solution of the equation.

Learn more about the algebraic expression here;

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