Question

Which sequence is modeled by the graph below?

A) an = one third(27)n − 1
B) an = 27(one third)n − 1
C) an = one third(3)n − 1
D) an = 3(one half)n − 1

Answer 1

We can see from points

(2,1) means for n = 2, a = 1

(3,3) means for n = 3, a = 3

(4,9) means for n = 4 , a= 9

Now try to see relation in outputs 1,3,9.

We can write 1 as
`3^(0)`

3 as
`3^(1)`

9 as
`3^(2)`

So (2,2) would mean for n =2, a = 1 or
`3^(0)`----------------(1)

(3,3) would mean for n = 3, a = 3 or
`3^(1)`-------------(2)

(4,9) would mean for n = 4, a = 9 or
`3^(2)`--------------------(3)

From (1) we can see for n =2, exponent on 3 is 0

From (2) we can see for n =3, exponent on 3 is 1

From (3) we can see for n =4, exponent on 3 is 2

So we can see the pattern whatever is n value its 2 less is the exponent on 3. So for n exponent on 3 will be n-2

For n = n, a =
`3^(n-2)`

Now looking at options given

option (A)
`(1)/(3) 27^(n-1)` doesnt match to
`3^(n-2)`

so its incorrect

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option (B)
`27(1)/(3)^(n-1)` doesnt match to
`3^(n-2)`

so its incorrect

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option (B)
`(1)/(3) 3^(n-1)` which we can also write as

`(3^(n-1))/(3) = (3^(n-1))/(3^(1)) = 3^(n-1-1) = 3^(n-2)`

we subtract exponents when dividing same bases so we subtracted exponent 1 from n-1 and finally got
`3^(n-2)`

so option (c) matches and is right answer

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option (D)
`3(1)/(2)^(n-1)` doesnt match to
`3^(n-2)`

so its incorrect