Write the following Arithmetic Sequence using a Recursive Formula: an = -7 + 3(n – 1) a1 = 3, an = an-1 – 7
a1 = -7, an = an-1 + 3
a1 = -7, an = an+1 + 3
a1 = 3, an = an+1 – 7

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  (b)  a[1] = -7, a[n] = a[n-1] + 3

Step-by-step explanation:

Comparing the given formula to the general form for the n-th term of an arithmetic sequence ...

  an = a1 +d(n -1)

we see that the first term (a1) is -7, and the common difference (d) is +3.

The recursive version of the sequence definition is ...

  a[1] = a1

  a[n] = a[n-1] +d

So, the appropriate choice is ...

  a[1] = -7, a[n] = a[n-1] +3

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.