Question

Write a rule for the arithmetic sequence.
5, 56, 107, 158, ...

Answer 1

What is the common difference?

Answer 2

To find the common difference of an arithmetic, just subtract a term from the next term.

Answer 3

the answers are, hold on.

Answer 4

A. A(n) = 5 + 51(n - 1)
B. A(n) = 5 + 51n
C. A(n) = 51 + 5(n - 1)
D. A(n) = 51 + 5n

Answer 5

Well, the sequence does start with 5, so the first 2 choices are a possibility.
The 3rd and 4th choices can be eliminated.

Answer 6

For the first term, n = 1.
Using choice A., you get A(1) = 5 + 51(1 - 1) = 5 + 51(0) = 5 + 0 = 5.
The first term is correct. Choice A is still possible.

Now let's try the first term with choice B.
Using choice A., you get A(1) = 5 + 51(1) = 5 + 51 = 5 + 51 = 56
This is not the first term, so choice B, is wrong.

The answer is A.