Question

How do you find the explicit definition for the sequence -2,1,4,7?

Answer 1

Notice how you're adding 3 to each term to get the next term (eg: -2+3 = 1 or 4+3 = 7)

So the common difference is 3

Answer 2

The first term is -2

Answer 3

I know that, I'm just not sure how to set it up

Answer 4

First term: a1 = -2
Common difference: 3


Plug these into an = a1 + d(n-1) to get the explicit rule


an = a1 + d(n-1)

an = -2 + 3(n-1)

an = -2 + 3n-3

an = 3n-5

Answer 5

So that's the formula you plug it into?

Answer 6

So let's say we wanted to find the 3rd term. That means n = 3

an = 3n - 5

a3 = 3*3 - 5

a3 = 9 - 5

a3 = 4

and 4 is indeed the 3rd term. I recommend you check the others.

Answer 7

yes it is

Answer 8

Wait Im lost, where did the 5 come from?

Answer 9

-2 - 3 is -5

Answer 10

Oh okay

Answer 11

look above in my steps and you'll see me jump from an = -2 + 3n-3 to an = 3n-5

Answer 12

So would the definition be an = -2 + (n+3) ?

Answer 13

no the definition is the last line

an = 3n - 5

Answer 14

basically the nth term is 3n - 5

Answer 15

where n is some positive whole number

Answer 16

Usually you have to simplify and combine like terms as much as possible

Answer 17

Im still kind of confused because these are the choices I have

Answer 18

oh they didn't simplify

Answer 19

how odd

Answer 20

then it would be an = -2 + 3(n-1)

Answer 21

all I did was plug in a1 = -2, d = 3 into an = a1 + d(n-1)

Answer 22

ohhhhhhhh ok

Answer 23

Ok i understand more now

Answer 24

again, the first term is a1 = -2, the common difference is d = 3

Answer 25

that's good