Question

PLEASE WALK ME THROUGH
In a geometric series with a common ratio of
-4 and whose initial value is -5 , the nth term is
equal to:
a. -4-5n
b. -5-4n
c. (-5*4 ) ^m (* MEANING "TIMES"/MULTIPLICATION :) )
d. (-5 )(-4 )^n
e. (-4 )(-5 )^n

Answer 1

It isn't any of these choices.

Answer 2

What do you think it is and why?

Answer 3

First off, given the type of answers listed, I think you are asking for the nth term of the sequence, not the series.

Answer 4

Second, the nth term of the sequence is:

(a)[r^(n-1)]

where "a" is the initial term and "r" is the common ratio. The first term has a factor of r^0, which makes the first term "a".

Answer 5

well, I am sorry. I have math questions for summer homework and this was what it said exactly. I need help understanding how to do it.

Answer 6

np. A series is going to be a sum like the following:

1 + x + x^2 + x^3 + . . . + x^n

And that is equal to [x^(n + 1) - 1] / (x - 1)

A sequence is a listing of numbers with no operation between them. So, the nth term of the sequence is:

(a)[r^(n-1)]

which here is:

(-5)[(-4)^(n-1)]

Answer 7

where does the -1 come in, in (n-1)?

Answer 8

That comes from the first term in the sequence has an exponent of "0" for the "r" as such:

(-5)[(-4)^0] = (-5)(1) = -5

And that's the initial term.

The second term has a "1" for the exponent. So, each term has "1 less" than the term number for the exponent value.

Answer 9

So, if you are at the "nth" term, the exponent on "r" is "one less" than "n". It is n-1.

Answer 10

Now, when we add up the terms in a sequence, we are then talking about a series.

Answer 11

I am sorry but I am not understanding what you are saying and how you even got (a)[r^(n-1)]

Answer 12

So, the closest answer you have to the correct answer is "d". But the exponent has to be "n-1", not "n".

Answer 13

okay.... well thank you so much for trying to help and explain, I really appreciate it.

Answer 14

(a)[r^(n-1)] is a formula used for generating a sequence. If you write this out you get:

(a)(r^0), (a)(r^1), (a)(r^2), (a)(r^3), . . .

which is

(a)(1), (a)(r^1), (a)(r^2), (a)(r^3), . . .

which is

a, (a)(r^1), (a)(r^2), (a)(r^3), . . .

For your sequence you have:

-5, +20, -80, +320 etc

Answer 15

@mary.rojas there is more explanation written here since you left.

Answer 16

I am still here. :)

Answer 17

np, so, the above tells you about the formula.

Answer 18

ok, i understand the formula. could you explain what "the common ratio means"
?

Answer 19

if you divide any term by the immediately previous term, you always get this common ratio.

Answer 20

That in part explains why the sign is alternating between + and -.

Answer 21

So, a (geometric) sequence is completely described by the common ratio and "a" which is the starting value.

Answer 22

ok :)

Answer 23

So, now, you might want to re-read post #8.

Answer 24

ok and yeah now this part makes since "The second term has a "1" for the exponent. So, each term has "1 less" than the term number for the exponent value."

Answer 25

Yes, and actually, I meant post #8 of the posts I wrote. Just look for the 8th occurrence of my icon.

Answer 26

ohh ok

Answer 27

So, I'm guessing that this is making a little more sense by now, @mary.rojas

Answer 28

now I understand the whole formula and the -1 and why the answer is not there really. Thank you so much. :)

Answer 29

You are very welcome!

Answer 30

Good luck in all of your studies and thx for the recognition! @mary.rojas

Answer 31

your welcome and thank you for the luck
:)