Answer:
Here we have the sequence:
6, 12, 18, 24
We can assume that this is an arithmetic sequence, this is, the difference between any two consecutive terms is always the same, D.
To check this, let's find the difference between the consecutive terms:
12 - 6 = 6
18 - 12 = 6
24 - 18 = 6
So we can conclude that this is an arithmetic sequence, and the difference between any two consecutive terms is always 6.
a) Then the next number in the sequence will be equal to the previous number plus 6, this is:
24 + 6 = 30
The next number in the sequence is 30
b) The term-to-term rule is the rule that defines the n-th term based on the previous terms.
Here we already know that each term in this sequence is the previous one plus six, so we can write this as:
Aₙ = Aₙ₋₁ + 6
c) The position-to-term rule is the general one.
Here we need to know that, the first term, A₁ = 6
Then, the n-th term will be A₁ plus (n - 1) times 6.
Then the rule is:
Aₙ = A₁ + (n - 1)*6
Replacing A₁ by its value, the rule becomes:
Aₙ = 6 + (n - 1)*6
