Question

Which sequence is modeled by the graph below?

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) $\frac{1}{3} 27^{n-1}$ doesnt match to $3^{n-2}$

so its incorrect

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option (B) $27\frac{1}{3}^{n-1}$ doesnt match to $3^{n-2}$

so its incorrect

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option (B) $\frac{1}{3} 3^{n-1}$ which we can also write as

$\frac{3^{n-1}}{3} = \frac{3^{n-1}}{3^{1}} = 3^{n-1-1} = 3^{n-2}$

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) $3\frac{1}{2}^{n-1}$ doesnt match to $3^{n-2}$

so its incorrect