Question

Given the sequence 7 comma 12 comma 17 comma 22 comma ellipsis



Which expression can be used to find the nth term in the sequence?

Answer options with 4 options
A.
2 n plus 5

B.
3 n plus 4

C.
4 n plus 3

D.
5 n plus 2

Answer 1

To find the nth term of the sequence 7, 12, 17, 22, ..., we first need to determine the pattern in the sequence.

The sequence has the following characteristics:

- The first term (n = 1) is 7.
- The second term (n = 2) is 12.
- The third term (n = 3) is 17.
- The fourth term (n = 4) is 22.

To find the common difference, we can subtract successive terms:

12 - 7 = 5
17 - 12 = 5
22 - 17 = 5

The common difference is 5, indicating that this is an arithmetic sequence.

The nth term of an arithmetic sequence can be found using the formula:
\[ a_n = a_1 + (n - 1) \cdot d \]
where \(a_n\) is the nth term, \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the term number.

For this sequence:
- \(a_1 = 7\)
- \(d = 5\)

Now, substituting these values into the formula:
\[ a_n = 7 + (n - 1) \cdot 5 \]
\[ a_n = 7 + 5n - 5 \]
\[ a_n = 5n + 2 \]

Thus, the expression to find the nth term of the sequence is:
\[ a_n = 5n + 2 \]

The correct answer is **D. 5n + 2**.