Question

Write a possible explicit formula for the following sequence...

Answer 1

\[-17,-22, -27, -32... A _{n} = ?\]

Answer 2

if n >=1(n is integer), then the general formula is -12-5n
if n >=0(n is integer), then the general formula is -17-5n
it all depends on n:)
the pattern is the next number decreases by 5

Answer 3

@mattt9

Answer 4

term 1 : -17
change in terms : -5
term 2: -22
term 3: -27

so..

x_n = -17 -5*(n-1)

Answer 5

So what would An =

Answer 6

An = x_n

they are the same thing

Answer 7

just a different notation

Answer 8

so -17 is the answer?

Answer 9

Your question asked for a formula not a number...

Your formula is:

An = (-17) - 5*(n-1)

where n is the nth term you are trying to determine.

So for example in the last question you asked where you wanted the 29th term. You could find the 29th term of this sequence by just plugging in 29 for n and solving for An

Answer 10

It all depends on your variable. n. if n >=0, then it starts from -17

Answer 11

ohhh hahahahahah totally had a blonde moment i got it now(: ty

Answer 12

but would there be such thing as a negative'th term in a sequence?

Answer 13

you would never refer to the negative 1th term

Answer 14

generally, it is not advisable to have a negative'th term. But if you wants, why not?
However, the standard norm is n should be a nonnegative integer or a positive integer.
So it is better for n to start from n>=0 or n>=1/（n is an integer)

Answer 15

I guess just how the problem was presented you are right to assume that the first term of the sequence would be -17

thus n is greater than or equal to 1

Answer 16

An = (-17) - 5*(n-1) is my answer ? correct?

Answer 17

yeah, that works for both of our cases haha

Answer 18

ok

Answer 19

thank you

Answer 20

It is correct plus you state that n is a positive integer(n>=1）

Answer 21

so An = (-17) - 5*(n-1)

Answer 22

Yes. It is better if you could simplify this expression to -12-5n:)

Answer 23

I'd personally leave it. It's easier to visualize in this form