Answer:
5,859,375
Step-by-step explanation:
pattern is x * 5
3, 15, 75, 375, 1875, 9375, 46875. 234375, 1171875, 5859375
[tex]10^{th}[/tex] term of the geometric sequence is [tex]\boldsymbol{5859375}[/tex].
A geometric progression, also known as a geometric sequence, is a non-zero numerical sequence in which each term after the first is determined by multiplying the preceding one by a fixed, non-zero value known as the common ratio.
Given geometric sequence is [tex]\boldsymbol{3,15,75}[/tex]
Ratio is [tex]r=\frac{15}{3}[/tex] that is [tex]\boldsymbol{r=5}[/tex].
[tex]n^{th}[/tex] term of a geometric sequence is given by [tex]\boldsymbol{ar^{n-1}}[/tex] where [tex]\boldsymbol{a}[/tex] is the first term.
So,
[tex]10^{th}[/tex] term of the geometric sequence [tex]=(3)(5)^{10-1}[/tex]
[tex]=(3)(5)^{9}\\=\boldsymbol{5859375}[/tex]
Find out more information about geometric series here:
https://brainly.com/question/3924955?referrer=searchResults
