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

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 as

9 as

So (2,2) would mean for n =2, a = 1 or ----------------(1)

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

(4,9) would mean for n = 4, a = 9 or --------------------(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 =

Now looking at options given

option (A) doesnt match to

so its incorrect

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option (B) doesnt match to

so its incorrect

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option (B) which we can also write as

we subtract exponents when dividing same bases so we subtracted exponent 1 from n-1 and finally got

so option (c) matches and is right answer

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option (D) doesnt match to

so its incorrect

7! = 7×6×5×4×3×2

3! = 3× 2

as 7! is multiple of 3! because 7! contains 3! that is 3× 2 as factor

so 7! /(3! ) = 7× 6× 5× 4

= 42 × 20

= 840

its b) 840✌✌✌

dhruv⭐