Question

Write an explicit formula for an,the Nth term of the sequence 4,12,36

Answer 1

`3^(n)+3^(n-1)`

Explanation:

Since the sequence is geometric (it multiplies the previous number each time). The nth term sequence would be
`x^n + yn`

Because the sequence multiplies by 3 each time, The base number in that equation would be
`3^n +yn`.

So
`3^n` of the equation would be:

`3, 9, 27`.

Compare the 2 equations:
4, 12, 36

3, 9 ,27

The difference between the 2 equations is: 1, 3, 9 which itself is a geometric sequence so the nth term of this new equation is:
`3^(n-1)`.

Combine these 2 equations together and you get:

`3^(n)+3^(n-1)`.