Question

Given the sequence -7, -3, 1, 5,What is the explicit formula to represent this sequence?A. a^n= 4n-7B. a^n= -7n+4C. a^n= 5-7nD. a^n= 4n-11

Answer 1

The given sequence is

`-7,-3,1,5`

To find the explicit formula, first, we have to find the difference by subtracting two consecutive terms.

`-3-(-7)=-3+7=4`

As you can observe, the difference is 4.

`d=4`

From the sequence, we observe that the first term is -7.

`a_1=-7`

The formula for arithmetic sequences is

`a_n=a_1+(n-1)d`

Now, let's replace the values we've got.

`a_n=-7+(n-1)\cdot4`

Then, we simplify.

`\begin{gathered} a_n=-7+4n-4 \\ a_n=4n-11 \end{gathered}`

Therefore, the right answer is D.