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

Group of answer choices

2, 5, 14, 41, 122...

2, 5, 8, 11, 14...

2, 3, 5, 11, 29, 86...

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

Answer 1

an=3+an-1

2, 5, 14, 41, 122..

9

Explanation:

Answer 2

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

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.