Remember that in a Geometric Sequence each term is found by multiplying the previous term by a constant.
In general, we write a geometric secuence as:
[tex]a,ar,ar^2,ar^3\ldots[/tex]Where:
• a, is the first term of the sequence
,• r ,is the common ratio (the factor between the terms)
For the particular sequence we're given, notice that we start at 4 and multiply by 3 in each step. This way,
[tex]\begin{gathered} a=4 \\ r=3 \end{gathered}[/tex]Therefore, the formula to calculate the value of the n-th step of the sequence is:
[tex]4\cdot3^{n-1}[/tex]For the ninth term (n = 9):
[tex]\begin{gathered} 4\cdot3^{9-1} \\ \rightarrow4\cdot3^8 \\ \Rightarrow26244 \end{gathered}[/tex]This way, the nith term of the geometric sequence is 26244
