Question

For the sequence -27, -12, 3, 18, ..., the expression that defines the nth term where a1 = -27 is

A. 15 --27n
B. 15-27 (n-1)
C. -27 + 15n
D. -27+15 (N-1)

Answer 1

The correct nth-term expression for the given sequence is -27 + 15(n - 1), reflecting the sequence's consistent increase of 15 between terms. So the correct option is D.

Step-by-step explanation:

The student's question asks for the expression that defines the nth term of the sequence -27, -12, 3, 18, ... given that a1 = -27. Observing the sequence, we can see that each term increases by 15 from the preceding term. Thus, to find the nth term, we start with the first term (-27) and add 15 to it n times (n - 1), because the first term is already included.

The correct expression for the nth term is therefore -27 + 15(n - 1), which simplifies to -27 + 15n - 15 and further simplifies to -42 + 15n. This corresponds to option D: -27 + 15 (n - 1).

Answer 2

D. -27+15 (N-1)

Step-by-step explanation:

-27, -12, 3, 18

Take the second term and subtract the first term to find the common difference

-12 - (-27)

-12+27 = 15

The common difference is +15

We are adding 15 each time

The formula for an arithmetic sequence is

an = a1+d(n-1)

an = -27 +15(n-1)