Question

Math Analysis:
Write an explicit formula for the nth term of the sequence.
18. 1, 1/3, 1/9, 1/27, 1/81

Answer 1

well, 3,9,27,81 look familiar to me

Answer 2

the 18. is a little off tho

Answer 3

no, this is the equation

Answer 4

do you know what a geometric sequence is?

Answer 5

no, i forgot lol

Answer 6

your times tables are geometric seqs. it is a sequence of numbers that are generated by multiply the same value to each term to get the next term

Answer 7

Tn=ar^n-1

Answer 8

that's the formula to find the indicated term of the geometric sequence i believe o-o

Answer 9

hmm, i might be confusing the issue in my head

your right about that being the general set up for a geo tho

this might be an arithmatic sequence

Answer 10

no, it geo ... im just getting too old lol

Answer 11

3*3 = 9
9*3 = 27
27*3 = 81

Answer 12

so, in your set up, a is the first term; and r is your common multiplier; or common ratio

Answer 13

common ratio is 1/3?

Answer 14

yep

Answer 15

Tn=1 x 1/3^n-1

Answer 16

redundant, but yes

Answer 17

the answer at the back says tn=3(1/3)^n

Answer 18

same thing

Answer 19

how?

Answer 20

youd have to remember rules for exponents to see the equalness about them

Answer 21

a^(m-n) = a^m * a^n

a^(-n) = 1/a^n

Answer 22

so my answer is correct? if i put that answer down on the test i won't get marked down cause this is for my final lol

Answer 23

1/3^(n-1) = 1/3^n * 1/3^(-1) = 1/3^n * 3

Answer 24

im not the one grading it

Answer 25

so my answer is wrong?

Answer 26

your answer is equivalent; but how your spose to get it to LOOK is up to the grader

Answer 27

some people dont wanna see negative exponents; others could care less

Answer 28

my teacher wants us to simplify our answers

Answer 29

idk if my answer was simplified

Answer 30

the 1x part is redundant, and can be simplified by ignoring it.

1x anything doesnt change its value

Answer 31

\[T_n=(\frac{1}{3})^{n-1}\]

rewrite it however you see fit

Answer 32

so now that answer is simplified?

Answer 33

.... there is no standard for "simplified". It is solely up to the person who is grading and what they have taught you

Answer 34

since i was not there, im wouldnt know

Answer 35

okay, but i think the answer on my answer sheet would be preferred by my teacher o-o

Answer 36

it should be :)

Answer 37

can you show me a way how to get tn=3(1/3)^n

Answer 38

i did, its posted above

Answer 39

what if i use this equation?
an= a + (n-1) d

Answer 40

use it for what?

Answer 41

for #18

Answer 42

since there is not "d" (common difference) between the terms; it would amount to trying to place a square peg into a round hole

Answer 43

so i use a different equation?

Answer 44

we have already used the appropriate equation; nothing else will work for it.

Answer 45

a^(m-n) = a^m * a^n

a^(-n) = 1/a^n

Answer 46

this one rite?

Answer 47

those are rules that govern exponents and how to rewrite this to fit your books answer

Answer 48

oh, so that was not an equation?

Answer 49

no, they werent. those are generalized rules for exponents that show you what you can do to them

Answer 50

ok, so why does 1/3^-1 turn into 3?

Answer 51

ohh, i get it haha :)

Answer 52

i use my calculator, but for this part i can't use my calculator

Answer 53

a negative exponent is a denominator is the simplest explanation i can think of

Answer 54

theres one part where i cant use a calculator for the test

Answer 55

so, if a number is to the -1 power u just put the number on the bottom to the top?

Answer 56

like 1/3

Answer 57

correct; we just flip the number

Answer 58

okay ty :)

Answer 59

1/3 ^ -1 flips to 3

yw