Question

Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.


n an
1 3
2 −6
3 12

Answer 1

an = −2(3)^n − 1 where n ≥ 3

an = −3(3)^n − 1 where n ≥ 3

an = 3(−2)^n − 1 where n ≥ 1

an = 3(−3)^n − 1 where n ≥ 1

Answer 2

@hartnn

Answer 3

find the common ratio 'r'

its is the ratio between consecutive terms

Answer 4

r= 2nd term/ 1st term = 3rd term/ 2nd term = ... ??

Answer 5

the only thing that i know is the formula
an=ar^n−1

Answer 6

i am pretty lost with this one so if you can explain

Answer 7

it would be helpful

Answer 8

r= 2nd term/ 1st term = 3rd term/ 2nd term

did you understand this part ?

Answer 9

what do you mean by 2nd term/ 1st term = 3rd term/ 2nd term??

Answer 10

n an ----- n is the index, an is the n'th term
1 3 ----index 1, so 1st term is 3
2 −6 ------index 2 means 2nd term is -6
3 12 -------index 3 means 3rd term is 12

Answer 11

now find the common ratio 'r'
since you now know 1st , 2nd and 3rd terms

Answer 12

\[\frac{ n_2 }{ n_1}\]
and
\[\frac{ n_3 }{ n_2 }\]

Is what is meant
Use the table to find the corresponding values of n

Answer 13

oh ok im getting there so r would be -2

Answer 14

thats correct!
and we already have
a = 1st term = 3

now just plug in values in the formula :)

Answer 15

3(-2)^n-1

Answer 16

\(\huge \checkmark \)

Answer 17

thanks

Answer 18

and n starts from 1
n = 1,2,3,4 ...
so, \(\Large n \ge 1 \)

Answer 19

welcome ^_^