Question

Which equation represents the sequence below?

10, 15, 20, 25, 30, . . .

(1 point)
Responses

y=10x+5y is equal to 10 x plus 5

y=5x+10y is equal to 5 x plus 10

y=−5x+10y is equal to negative 5 x plus 10

y=5x+5

Answer 1

To find the equation that represents the sequence 10, 15, 20, 25, 30, ..., we first identify the pattern in the sequence.

The sequence begins at 10 and increases by 5 each time:
- \(10 + 5 = 15\)
- \(15 + 5 = 20\)
- \(20 + 5 = 25\)
- \(25 + 5 = 30\)

This indicates that the sequence has a common difference of 5, which is characteristic of an arithmetic sequence.

To find the equation of this linear sequence, we can use the formula for the \(n\)-th term of an arithmetic sequence:
\[
y = mx + b
\]
where \(m\) is the common difference and \(b\) is the first term.

Here, the common difference \(m\) is 5 and the first term (when \(x = 1\)) is 10. We can substitute these values into the equation:

1. For \(x = 1\): \(y = 5(1) + b\) should equal 10.
\[
5 + b = 10 \implies b = 5
\]

Now we can write the equation as:
\[
y = 5x + 5
\]

So, the correct equation that represents the sequence is:
**y = 5x + 5.**