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

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)

its 50 miles away from the starting point