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Mandarinka [93]
3 years ago
9

Write the explicit rule for the nth term. Then find a21 {4, 16, 64...}

Mathematics
1 answer:
oksian1 [2.3K]3 years ago
3 0

Answer:

The rule would be 4ⁿ

4²¹

Step-by-step explanation:

This is a geometric sequence, the terms are all powers of 4.

The rule here would be 4ⁿ

To find the 21st term, we simply substitute 21 for n in our rule. So:

= 4²¹

Leaving in index form is fine as the expanded number is very large

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If(√14/√7-2)-(√14/√7+2)=a√7+b√2 find the values of a and b where a and b are rational numbers​
seraphim [82]

Answer:

  • a = 4/3 and b = 0

============================

<h2>Given expression:</h2>

\dfrac{\sqrt{14} }{\sqrt{7}-2} -\dfrac{\sqrt{14} }{\sqrt{7}+2}

<h2>Simplify it in steps:</h2>

<h3>Step 1</h3>

Bring both fractions into common denominator:

\dfrac{\sqrt{14} (\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} - \dfrac{\sqrt{14} (\sqrt{7}-2)}{(\sqrt{7}-2)(\sqrt{7}+2)}

<h3>Step 2</h3>

Simplify:

\dfrac{\sqrt{14} ((\sqrt{7}+2) - (\sqrt{7}-2))}{(\sqrt{7}-2)(\sqrt{7}+2)} =

\dfrac{\sqrt{14} (\sqrt{7}+2 - \sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} =

\dfrac{4\sqrt{14} }{(\sqrt{7}-2)(\sqrt{7}+2)} =

\dfrac{4\sqrt{14} }{(\sqrt{7})^2-2^2} =

\dfrac{4\sqrt{14} }{7-4} =

\dfrac{4}{3}  \sqrt{14} }

<h3>Step 3</h3>

Compare the result with given expression to get:

  • a = 4/3 and b = 0

4 0
2 years ago
Based on a kc value of 0.200 and the given data table, what are the equilibrium concentrations of xy, x, and y, respectively?
MariettaO [177]
There is no given data table but based on the question, the reaction is
xy <=> x + y
If we let M as the initial concentration of xy and c as the in the concentration after the dissociation, then we can use the ICE method
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I    M
C  -c            c         c
-----------------------------
E  M-c          c         c

Solve for c using
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And the concentration of the xy, x, and y can then be determined
3 0
4 years ago
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Bingel [31]

Answer:

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Step-by-step explanation:

3 0
3 years ago
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Best of Luck!

7 0
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Answer:

What do you mean

Step-by-step explanation:


7 0
4 years ago
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