An arithmetic sequence has a third term of 7 and a fifth term of 13. write an equation could be used to find the both term of the sequence.

a(n) = 3n - 2.

Step-by-step explanation:

The nth term of an arithmetic sequence = a1 + d(n - 1)  where a1 = the first term and d = the common difference.

So here we  have:

a3 = 7 = a1 + 2d

a5 = 13 = a1 + 4d

Rewriting:

a1 + 4d = 13

a1 + 2d = 7  

Subtracting,  we eliminate a1:

2d = 6

d = 3

and a1 = 7 - 2(3)

= 1.

So our equation we can use to find any term is

a(n) = 1 + 3(n - 1)

a(n) = 1 + 3n - 3

a(n) = 3n - 2 (answer).

Checking :

3rs term = 3(3) - 2 = 7.

5th term = 3(5) - 2 = 13.

First term = 3(1) - 2 = 1.

D) A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin.

Step-by-step explanation:

Given is the graph of ABC and A'B'C'.

We can take reference of parallel lines AB and A'B', it means the shape is rotated 180 degrees counterclockwise.

For A'B'C' to be in third quadrant, its original shape must be in first quadrant. It means ABC should be translated to first quadrant.

Checking the given options, we can say ABC is translated 5 units to the right (towards first quadrant), followed by a 180 degree counterclockwise rotation about the origin (resulting in third quadrant).

Hence, option D is correct.