Question

Which sequences could be described by the recursive definition LaTeX: a_{n+1}=3\cdot a_n-1a n + 1 = 3 ⋅ a n − 1

Answer 1

Answer:

an=3+an-1

2, 5, 14, 41, 122..

9

Step-by-step explanation:

Answer 2

Answer:

2,6,18,54,162...

Step-by-step explanation:

The given expression is:

$a_{n}=3 a_{n-1}$

To find the right sequence, we have to find the value for $n=1$, $n=2$, $n=3$, $n=4$ and $n=5$, which are presented in the following operations, also we know that the first term is 2, we can begin from there:

$a_{1}=2\\a_{2}=3(2)=6\\ a_{3}=3(6)=18\\ a_{4}=3(18)=54\\ a_{5}=3(54)=162$

As you can see, the given expression represents a sequence where the next term is the triple than the term before.

As a result, we found the sequence 2, 6, 18, 54, 162...

Therefore the right answer is the last choice.