Question

Find an equation for the nth term of the sequence.

-4, -16, -64, -256, ...

Answer 1

@Compassionate

Answer 2

@iambatman @Ashleyisakitty

Answer 3

well the sequence is geometric... do you know the common ratio...?

Answer 4

\(\large\color{black}{ a_n=a_1\times r^{n-1} }\) this is the equatioon you need to find.
You just need to determine the \(\large\color{black}{ a_1 }\) and the \(\large\color{black}{ r }\) .

Answer 5

( \(\large\color{black}{ a_1 }\) is the first term of the sequence.)
( \(\large\color{black}{ r }\) is the common ratio of the sequence. )

Answer 6

Yea thats what I have in my notes but the answers dont show it with the ^ part

Answer 7

what do you mean don't show it when the ^ part? yu mean you don't have the \(\large\color{black}{ r^{\color{red}{n-1}} }\) (in red) ?

Answer 8

not when, it is with.

Answer 9

yea there isnt that

Answer 10

well, you either need the: \(\large\color{blue}{ a_n=a_1\times r^{n-1} }\) or \(\large\color{green}{ a_n=a_{n-1}\times r }\) .

Answer 11

let me try to work it out though

Answer 12

then would it be an = -4 • 4^n - 1

Answer 13

yes, it is exactly that: Just making sure you meant what I thought you mean. (lol)
\(\large\color{red}{ a_n=(-4)\times4^{n-1} }\)

Answer 14

that is correct.

Answer 15

Oh okay cool thanks :)

Answer 16

Anytime....!

Answer 17

Find an equation for the nth term of the arithmetic sequence.

-17, -14, -11, -8, ...
For this one can you check my answer

Answer 18

an = -17 + 3(n - 1)
@SolomonZelman

Answer 19

@SolomonZelman

Answer 20

yup, that's is right again:)

Answer 21

but this time there is no ^ ?

Answer 22

yes, there is no ^.

Answer 23

when do I know when there will be a ^

Answer 24

I lost connection.

Answer 25

Okay, so in any arithmetic sequence you know that the pattern is:
\(\large\color{black}{ a_1\times r=a_2 }\)
\(\large\color{red}{ a_1\times r^2=a_3 }\)
\(\large\color{black}{ a_1\times r^3=a_4 }\)
\(\large\color{red}{ a_1\times r^4=a_3 }\)

you are multiplying times the common ratio each time. that is why you have the ^.

Answer 26

the last red row is supposed to be a5 at the end, not a3.

Answer 27

Okay, now, an arithmetic sequence. You are adding the common difference and this is what happens.
\(\large\color{black}{ a_1+ d=a_2 }\)
\(\large\color{red}{ a_1+2d=a_3 }\)
\(\large\color{black}{ a_1+3d=a_4 }\)
\(\large\color{red}{ a_1+4d=a_5 }\)

that is why you don't have the ^.

Answer 28

Oh okay so depending on how the question is asked whether arithmetic or geometric

Answer 29

yes.

Answer 30

oh okay thankyou

Answer 31

You welcome!