Question

what are the explicit equation and domain for a geometric sequence with a first term of 5 and a second term of -10

Answer 1

@Hero @ganeshie8

Answer 2

@SolomonZelman @jim_thompson5910

Answer 3

5r = -10

r = ???

Answer 4

-2

Answer 5

First Term: a = 5
Common Ratio: r = -2

Plug those into

\[\Large a_{n} = a*(r)^{n-1}\]

to get the general nth term formula

Answer 6

5n = 5 x (-2) n-1

5n = -10 n-1

What do i do from here

Answer 7

no a_n symbolizes the n term of the sequence
a_n and a are different values
also we don't have (ar)^(n-1)
we just have that the r is to the (n-1)

Answer 8

Ok, so how do i set up this equation

Answer 9

\[a_n=a \cdot r^{n-1}\]

just replace the a with 5 and replace the r with -2 like jim said

Answer 10

5n = -10^n-1
?

Answer 11

again a_n and a are different values
a_n is a variable by itself
you can't multiply a and r
because r has an exponent

Answer 12

5_n = 5 x -2^n-1

Answer 13

you cannot replace a_n with 5_n
this makes no sense


let me show you how this formula is come up with so maybe you understand better

{a_n} is a sequence of numbers

those numbers are
a_1=5
a_2=5(-2)=-10
a_3=5(-2)(-2)=5(-2)^2=20
a_4=5(-2)(-2)(-2)=5(-2)^3=-40
a_5=5(-2)(-2)(-2)(-2)=5(-2)^4=80
...
therefore a_n=5(-2)(-2)(-2)(-2)(-2)(-2)...(-2)=
(by the way that is a (n-1) amount of (-2))

I put a (n-1) amount of (-2)

because looking at a_1 we have (-2)^0=(-2)^(1-1)
looking at a_2 we have (-2)^1=(-2)^(2-1)
looking at a_3 we have (-2)^2=(-2)^(3-1)

it is always one less than where the number is in the sequence

Answer 14

So how do i set up the equation ? im confused

Answer 15

Does the 5 not go where the n is

Answer 16

5 goes where 'a' is

but \(\Large a_n\) is NOT the same as just 'a'

Answer 17

If it confuses you, think of it as

\[\Large T = a*(r)^{n-1}\]

T = nth term
a = first term
r = common ratio
n = positive whole number (used to identify which term you're dealing with)

example: n = 3 ---> 3rd term

Answer 18

Ok

Answer 19

The notation \(\Large a_n\) is used for sequences because the 'n' changes to a positive whole number to indicate a certain term

example: 17th term ---> n = 17 ---> \(\Large a_n = a_{17}\)

Answer 20

Ok, so you leave the an as it is

Answer 21

Yep it is a formula for the nth term in the sequence

Answer 22

So it is an = 5 (-15)^n-1; all integers where n less than or equal to 1

Answer 23

how do you get -15 for r?

Answer 24

r symbolizes the geometric ratio
to find r all you have to do is evaluate a_2/a_1

or take any two consecutive numbers in the sequence and put the 2 nd term of those numbers over the 1st term of those numbers

Answer 25

also this was already determined way above when joe was working with you

Answer 26

the answer is A!!!!!!!!!!!!!!!!!