Question

What is the explicit formula for this sequence?

-7,-3, 1, 5,...

A. an = -7 + (n - 1)(-4)
B. an = 9+ (n - 1)(-4)
C. an = -7 + (n - 114
D. an= -4 + (n - 1)(-7

Answer 1

`a_n=-7+4(n-1)`

or

`a_n=-7+(n-1)(4)`

Explanation:

-7,-3,1,5,... is a arithmetic sequence.

Arithmetic sequences have a common difference. That is, it is going up by 4 each time.

When you see arithmetic sequence, you should think linear equation.

The point-slope form of a line is
`y-y_1=m(x-x_1)`.

m is the common difference, the slope.

Any they are using the point at x=1 in the point slope form. So they are using (1,-7).

So let's put this into our point-slope form:

`y-(-7)=4(x-1)`

`y+7=4(x-1)`

Subtract 7 on both sides:

`y=-7+4(x-1)`

So your answer is

`a_n=-7+4(n-1)`