Question

Write the Explicit Rule for the arithmetic sequence:Qp = Q1 +(n-1)d8, 5, 2, -1, ...​

Answer 1

Answer:

Last choice.

Step-by-step explanation:

8, 5, 2, -1, ...​

Make a table

n            |      1            2             3           4          5  

an          |      8           5             2           -1         -4

You really should just think of this as finding the equation of a line.

The slope can be used by using any two points.

How about

(1  ,  8)  and

(2 ,  5)?

------------I really like to find the slope by lining up my points and subtracting vertically and then putting second number on top of first.

That is the same as using the formula directly which is (y2-y1)/(x2-x1)

or (y1-y2)/(x1-x2) which gives you the same thing too.

Subtracting the pairs now:

(1  ,  8)

-(2 ,   5)

-----------

-1       3

So the slope is 3/-1 or -3/1 or -3.

So you can already rule out choice B.

So we have the equation is y=-3x+b

where y really represents an and x really represents n here.

You can use any point that you know is on the line to find b.

How about (1,8)?

Plug it into y=-3x+b.

y=-3x+b

8=-3(1)+b

8=-3+b

11=b

So the line is y=-3x+11

Want to confirm?

No problem:

At x=1 you have y=-3(1)+11=-3+11=8 which is first number in the list.

At x=2 you have y=-3(2)+11=-6+11=5 which is second number in the list.

At x=3 you have y=-3(3)+11=-9+11=2 which is the third number in the list.

At x=4 you have y=-3(4)+11=-12+11=-1 which is the fourth number in the list.

So we have confirmed our solution of y=-3x+11.

So the answer is an=-3n+11