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3 years ago

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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Answer:

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

<h2>Given expression:</h2>

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

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

Bring both fractions into common denominator:

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

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Compare the result with given expression to get:

a = 4/3 and b = 0

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