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3 years ago

What is the 31st term of the sequence below? -108, -90, -72, -54, ...

Mathematics

1 answer:

Harrizon [31]3 years ago

3 0

Answer:

Step-by-step explanation:

The form for finding the nth term of an arithmetic sequence is a(n) = b +(n-1)d, where a is the function of the nth term, b is the first number in the sequence, n is the nth term, and d is the common difference. Plugging in what we know we get:

a(31) = -108 + 30 x 18

multiply

a(31) = -108 + 540

add

a(31) = 432

<em>PLEASE MARK BRAINLIEST</em>

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2 years ago

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Answer:

$A=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}$

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Step-by-step explanation:

It is given that the snack shop makes 3 mixes of nuts in the following proportions.

Mix I: 6 lbs peanuts, 2 lbs cashews, 2 lbs pecans.

Mix II: 5 lbs peanuts, 3 lbs cashews, 2 lbs pecans.

Mix III: 3 lbs peanuts, 4 lbs cashews, 3 lbs pecans.

they received an order for 25 of mix I, 18 of mix II, and 35 of mix III.

We need to find the matrices A & B for which AB gives the total number of lbs of each nut required to fill the order.

Mix I Mix II Mix III

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cashews 2 3 4

pecans 2 2 2

$A=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}$

$B=\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}$

The product of both matrices is

$AB=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}$

$AB=\begin{bmatrix}6\cdot \:25+5\cdot \:18+3\cdot \:35\\ 2\cdot \:25+3\cdot \:18+4\cdot \:35\\ 2\cdot \:25+2\cdot \:18+3\cdot \:35\end{bmatrix}$

$AB=\begin{bmatrix}345\\ 244\\ 191\end{bmatrix}$

Therefore matrix AB gives the total number of lbs of each nut required to fill the order.

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