EnoughEnoughNow
contestada

For the following geometric sequence, find the recursive formula and the 5th term in the sequence. In your final answer, include all of your work.
{-4, 12, -36, ...}

Respuesta :

...42, -193.. thats the 4th and 5th
manuelatuozzo

Answer:

[tex]a_n = (-3) *a_{n-1} \\ a_5 = -324[/tex]

Step-by-step explanation:

Let's remember the definition of geometric sequence:

Each term is found by multiplying the previous term by a constant.  

We need to find out that constant. As it's always the same, we just need to divide the second term by the first one to get it.

[tex]12/-4 = -3[/tex]

The recursive formula will be:

[tex]a_1 = -4 \\ a_n = (-3) *a_{n-1}[/tex]

With this, to find the 5th term in the sequence we need the fourth one first

[tex]a_4 = (-3) *a_3 = (-3) *(-36) = 108\\ a_5 = (-3) *a_4 = (-3) *108 = -324[/tex]

[tex]a_5 = -324[/tex]