Question

Write an expression for the nth term of the sequence

Answer 1

hint: focus just on the pattern going on in the numerator (ignore the denominator). Then focus on the pattern going on in the denominator (ignore the numerator)

Answer 2

numerator= +1
denominator= x3

Answer 3

so just focusing on the numerator, how can we write a rule for it (using a variable)?

Answer 4

an= n+3/3^n

Answer 5

I'm assuming you mean

\[\Large a_{n} = \frac{n+3}{3^{n}}\]

let's check

if we start at n = 1, then


n = 1 ---> n+3 = 1+3 = 4 ... works
n = 2 ---> n+3 = 2+3 = 5 ... works
n = 3 ---> n+3 = 3+3 = 6 ... works
I'm sure you see that it also works for n = 4, n = 5, etc

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In the denominator

n = 1 ---> 3^n = 3^1 = 3 ... works
n = 2 ---> 3^n = 3^2 = 9 ... works
etc etc

So we can see that this rule works out

Answer 6

yay :) thanks