Construct a recursive rule to describe the sequence: 2, 4, 6,

  a[1] = 2; a[n] = a[n-1] + 2

Step-by-step explanation:

The first term of the sequence is 2, so the first part of the definition is ...

  a[1] = 2

Each term is 2 more than the previous one, so the rest of the definition is ...

  a[n] = a[n-1] + 2

Comment on recursive rules

A recursive rule has two parts. The first part tells what the initial value of the sequence is. The second part relates the next term to the previous term or terms.

For arithmetic and geometric sequences, each term is related to the previous term by a constant. For an arithmetic sequence, each term is the last term plus the common difference. For a geometric sequence, each term is the last term multiplied by the common ratio.

It must have the same slope as the given line, so

m = -A/B = -1/-2 = 1/2

So far, we have

y = mx + b = x/2 + b

Use the given point to find b.

4 = -2/2 + b = -1 + b

b = 5

y = x/2 + 5

Multiply through by 2.

2y = x + 10

Standard form:

x - 2y = -10