Question

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

Answer 1

Answer:

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)

Answer 2

So the formula for an arithmetic sequence (where you're adding or subtracting by the same number each time) is $a_{n}$ = $a_{1}$ + d(n - 1)

In this equation:

$a_{n}$ is the nth term

$a_{1}$ is the first term

d is the common difference (the number you're adding or subtracting each time)

n is the number of the term (e.g. 1st term, 2nd term, 3rd term etc)

So we're given that $a_{1}$ = -27, and we can find that d = 15 (because we add 15 each term). We just plug these values into the equation to get...

$a_{n}$ = -27 + 15 (n - 1)

It looks like that's your answer, D. But if you needed to solve it out further, you could:

We can use the distributive property...

$a_{n}$ = -27 + 15n - 15

Then combine like terms...

$a_{n}$ = 15n - 42

Hope that helps! Feel free to message me if you need clarification