To determine the nth term [tex]\( a_n \)[/tex] of the geometric sequence with an initial term [tex]\( a_1 = 8.5 \)[/tex] and a common ratio [tex]\( r = 7 \)[/tex], you can use the formula for the nth term of a geometric sequence:
[tex]\[ a_n = a_1 \cdot r^{(n-1)} \][/tex]
Here's the step-by-step process:
1. Identify the initial term [tex]\( a_1 \)[/tex] and the common ratio [tex]\( r \)[/tex]:
- [tex]\( a_1 = 8.5 \)[/tex]
- [tex]\( r = 7 \)[/tex]
2. Write the general formula for the nth term of a geometric sequence:
The nth term formula is expressed as:
[tex]\[ a_n = a_1 \cdot r^{(n-1)} \][/tex]
3. Substitute the known values into the formula:
- The initial term [tex]\( a_1 = 8.5 \)[/tex]
- The common ratio [tex]\( r = 7 \)[/tex]
This gives us:
[tex]\[ a_n = 8.5 \cdot 7^{(n-1)} \][/tex]
Therefore, the nth term of the geometric sequence is given by the formula:
[tex]\[ a_n = 8.5 \cdot 7^{(n-1)} \][/tex]
This formula can now be used to find any term in the sequence by substituting the value of [tex]\( n \)[/tex].
