Question

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

Answer 1

Answer:

$3^{n}+3^{n-1}$

Step-by-step 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:

$3^{n}+3^{n-1}$.