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3 years ago

Write a recursive rule for the sequence. Assume it starts with the 1st term. 10, 14, 18, 21...

Mathematics

1 answer:

Papessa [141]3 years ago

3 0

Option D is correct. The correct option for the recursive formula is $f(0) =6;f(n)=f(n - 1)+4$

Given the sequence 10, 14, 18...

The first term is 10, hence

a1 = 10

The previous terms will be $a_{n-1}$

From the sequence, we can see that <em>4 is being added to the previous term to get the next term</em>. Hence the nth term will be expressed as:

$a_n = a_{n-1} + 4$

Get the term before the first term $a_0$

If n = 1

$a_1 = a_{1-1} + 4\\a_1 = a_{0} + 4\\a_0=a_1-4\\a_0=10-4\\a_0=6$

Hence the correct option for the recursive formula is $f(0) =6;f(n)=f(n - 1)+4$

Learn more here: brainly.com/question/18233843

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A rectangular prism had a volume of 252 cubic centimeters. The length of the prism is 14 centimeters and the width of the prism

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<h2>Answer:</h2>

A prism is a solid object having two identical bases, hence the same cross section along the length. Prism are called after the name of their base. A rectangular prism is a solid whose base is a rectangle. Multiplying the three dimensions of a rectangular prism: length, width and height, gives us the volume of a prism:

$V=L\times W\times H$

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$L=14cm \\ \\ W=6cm \\ \\ H=3cm$

In fact, the volume is $252cm^3$ because:

$V=14\times 6\times 3 \therefore V=252cm^3$

Now the height of the prism was changed from 3 centimeters to 6 centimeters to create a new rectangular prism, therefore:

FOR THE NEW PRISM WE HAVE THE FOLLOWING DIMENSIONS:

$L=14cm \\ \\ W=6cm \\ \\ H=6cm$

So the new volume is:

$V=14\times 6\times 6 \therefore V=504cm^3$

<h3><em>What do we know about the volume of the new prism?</em></h3>

<em>Well, the volume has increased from </em> $252cm^3 \ to \ 504cm^3$ <em>and since</em> $504=2\times 252$ <em>we can say that the new volume is two times the original volume.</em>

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