Question

For the sequence -3, 3, 9, 15, 21, what is the equation in the form y=−2+6(n−1)?

a) y=−2+6n
b) y=−2+6n−1
c) y=−2+6n−2
d) y=−2+6n+1

Answer 1

In the sequence -3, 3, 9, 15, 21, the correct equation is b) y = -2 + 6n - 6, which simplifies to y = 6n - 8. This equation matches the initial term and the constant difference between terms in the sequence.

Step-by-step explanation:

The question asks for the equation of a sequence in the form y = -2 + 6(n-1). To find the correct equation, we can analyze the given sequence: -3, 3, 9, 15, 21.

Firstly, note that the sequence increases by 6 each time, which aligns with the 6(n-1) part of the equation. Now, we need to determine the starting value when n=1 to ensure the equation fits the sequence correctly.

When n=1, the equation y = -2 + 6(n-1) simplifies to y = -2. However, the first term of the sequence is -3, not -2. Therefore, we need to adjust the initial value to match the sequence.

By inspecting the options, we see that option b) y = -2 + 6n - 6 fits. When n=1 for option b: y = -2 + 6(1) - 6 = -2, which matches the first term of the sequence. As we increase n, the value of y will increase by 6 for each subsequent term, matching the pattern of the sequence.

Therefore, the correct equation is b) y = -2 + 6n - 6, which can be simplified to y = 6n - 8.