To find the nth term of the geometric sequence with the given initial term [tex]\( a_1 = 8.5 \)[/tex] and common ratio [tex]\( r = 7 \)[/tex], we can use the formula for the nth term of a geometric sequence. The formula is given by:
[tex]\[
a_n = a_1 \cdot r^{(n-1)}
\][/tex]
where:
- [tex]\( a_n \)[/tex] is the nth term we want to find,
- [tex]\( a_1 \)[/tex] is the first term of the sequence,
- [tex]\( r \)[/tex] is the common ratio, and
- [tex]\( n \)[/tex] is the term number.
Given [tex]\( a_1 = 8.5 \)[/tex] and [tex]\( r = 7 \)[/tex], we substitute these values into the formula:
[tex]\[
a_n = 8.5 \cdot 7^{(n-1)}
\][/tex]
Therefore, the nth term of the geometric sequence, [tex]\( a_n \)[/tex], as a function of [tex]\( n \)[/tex], is:
[tex]\[
a_n = 8.5 \cdot 7^{(n-1)}
\][/tex]
