Question

Consider the following geometric sequence 2,6,18,54what is the recursive and explicit formula?

Answer 1

Answer:

       

Step-by-step explanation:

The given geometric sequence is:

2,6,18,54

Here, $a_{1}=2$, $a_{2}=6$, $a_{3}=18$ and $a_{4}=54$

Explicit formula is given as: $a_{n}=a_{1}r^{n-1}$

Now, $r=\frac{a_{n+1}}{a_{n}}$

=$\frac{6}{2}=3$

Substituting in the above explicit formula, we have

$a_{n}=2(3)^{n-1}$

=$2(3)^n(3)^{-1}=\frac{2}{3}(3)^n$

Recursive formula is given as:$a_{1}=2$, $a_{n+1}=3a_{n}$.

Answer 2

Recursive:
a(1)≈2
a(n)≈a(n-1)x3

explicit:
a(n)≈ 2(3)^n-1