Question 1198628
<font color=black size=3>
Answer: <font color=red>3   (choice C)</font>


Explanation:


Refer to this previous similar question.
<a href = "https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1198622.html">https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1198622.html</a>
In it I discuss that this sequence is geometric with
a = 5 = first term
r = -2/3 = common ratio


I then further explained that
S = a/(1-r)
S = 5/(1-(-2/3))
S = 3
represents the summation of the infinitely many terms.


The formula
S = a/(1-r)
only works when -1 < r < 1 is true.
Otherwise, the geometric series would diverge.


Luckily -1 < -2/3 < 1 is true, so -1 < r < 1 is true for r = -2/3.
</font>