Question

or Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 9, 18, 27, 36, ...

Answer 1

The sequence provided is an arithmetic sequence where each term increases by a common difference of 9. The expression that represents the sequence based on the term's position n is an = 9n.

Step-by-step explanation:

The sequence given is 9, 18, 27, 36, ... which can be described by an arithmetic sequence formula where each term increases by a common difference.

Since the common difference is 9, we can construct the expression based on the position of a term represented by n, where n = 1 for the first term.

The expression can be found by multiplying the common difference by n and then adding the first term subtracted by the common difference.

So, the expression for the nth term (an) of the sequence is: an = 9n.

This is because 9 times the position of the term gives the value of that term in this arithmetic sequence.

For example, for the first term where n = 1, the value is 9 times 1, which equals 9.

Similarly, for the second term where n = 2, the value is 9 times 2, which equals 18, and so on.