The nth term of a sequence is n^2 -n-2 .find the sum of the first and third terms

Mathematics

1 answer:

Troyanec [42]4 years ago

8 0

Answer:

Step-by-step explanation:

substitute n=1 and n=3 in the given equation

1 st term is (1)^2-1-2 = 1 -1 -2 = -2

3rd term is (3)^2-3-2 = 9-3-2=4

sum of 1st and 3rd term is -2 + 4 = 2

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The best correct option is option D), (the y-coordinate for the point (8, -7) is to be replaced with a 7 to give (7, -7) as follows:

$\left[\begin{array}{rrrr}1&0\\0&-1\end{array}\right] \left[\begin{array}{rrrr}9&7&3&2\\-3&-7&-7&-5\end{array}\right]$

The reason the above matrix value for the matrix operation are correct are as follows:

Known parameters:

From the diagram, we have that the coordinates of the vertices of the preimage are;

(2, -5), (3, -7), (9, -3), and (7, -7)

The coordinates of the vertices of the image are;

(2, 5), (3, 7), (9, 3), and (7, 7)

Required:

The matrix operation for the transformation of the preimage points to the image points

Solution:

The transformation from the coordinates of the vertices of primage to the vertices of image involves the change in the sign from negative to positive, of the y-values of the image, which can be obtained by multiplying by (-1)

Therefore, the required matrix operation is presented as follows:

$\mathbf{\left[\begin{array}{rrrr}1&0\\0&-1\end{array}\right] \left[\begin{array}{rrrr}9&7&3&2\\-3&-7&-7&-5\end{array}\right]} =\left[\begin{array}{rrrr}9&7&3&2\\3&7&7&5\end{array}\right]$