The rule for being the nth item in a certain sequence is n(n+1)/2. what is the 4th term in this sequence ?

Mathematics

1 answer:

Lorico [155]3 years ago

7 0

Answer:

a.) 4

Step-by-step explanation:

a.)4

You might be interested in

What is the domain of this function in the graph below? <br><br> What is the interval?

Maurinko [17]

Domain in interval: [6,infinity)

5 0

3 years ago

-x=-y+2 and 3y+4=2x solve using matrices

MissTica

$\begin{cases}-x=-y+2\\3y+4=2x\end{cases}\implies\begin{cases}x-y=-2\\2x-3y=4\end{cases}$

In matrix form, this is

$\begin{bmatrix}1&-1\\2&-3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-2\\4\end{bmatrix}$

The coefficient matrix has determinant

$\begin{vmatrix}1&-1\\2&-3\end{vmatrix}=-3+2=-1\neq0$

so it has an inverse, which is

$\begin{bmatrix}1&-1\\2&-3\end{bmatrix}^{-1}=\begin{bmatrix}3&-1\\2&-1\end{bmatrix}$

Multiply both sides by the inverse matrix:

$\begin{bmatrix}3&-1\\2&-1\end{bmatrix}\begin{bmatrix}1&-1\\2&-3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}3&-1\\2&-1\end{bmatrix}\begin{bmatrix}-2\\4\end{bmatrix}$

$\implies\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-10\\-8\end{bmatrix}$

so that $x=-10$ and $y=-8$ .

8 0

4 years ago

What is the common ratio in the following geometric sequence?

VARVARA [1.3K]

Hey there!

A common ratio is just that number that you multiply or divide to each number that gets you the next in a geometric sequence. In this sequence, we know the numbers are getting bigger and we're multiplying, so we want to know what you're multiplying by the first number to get to the second. We can call this unknown number x. SO if we start with the first number and set up an equation, we get:

3x = 12

Divide both sides by 3

x = 4

Therefore, your common ratio is 4.

To check, you can multiply all the next numbers by 4 to see that it all checks out.

Hope this helps!

3 0

3 years ago

The interior angle measures of a convex pentagon are consecutive multiples of 4. find the measure of each interior angle.

lawyer [7]

Answer:

100°, 104°, 108°, 112°,116°