Question

Guided Practice

3. Write an equation for the nth term of the geometric sequence 96, 48, 24, 12, ---
Then find the tenth term of the sequence.
Remember to use the formula at the top of the page and substitute.

Answer 1

Ah! Geometric sequences, Eh? Sucks I know....

Explanation:

So first, we need to find the factor of this(been a while since I have done this)

`r=(24)/(48) =(1)/(2)`

So we found the relationship! Now we find the entire equation.

So we know the first term, 96, so let's use it!

`a_(n) =96*((1)/(2))^(n-1)`

So there is the equation!

Now to find the 10th term.

`a_(n) =96*((1)/(2))^(n-1)\\a_(10) =96*((1)/(2))^(9)\\a_(10) =96*(1)/(2^(9) ) \\a_(10)=0.1875`

There you have it!

Hope this Helps!

P.S. Stay Safe!