Answer :
We start by identifying the first term of the sequence:
[tex]$$a_1 = 60.$$[/tex]
Next, we find the common ratio by dividing the second term by the first term. The second term is:
[tex]$$a_2 = 12.$$[/tex]
Thus, the common ratio is:
[tex]$$r = \frac{a_2}{a_1} = \frac{12}{60} = \frac{1}{5}.$$[/tex]
For any geometric sequence, the explicit formula for the [tex]$n$[/tex]th term is given by:
[tex]$$a_n = a_1 \cdot r^{n-1}.$$[/tex]
Substituting the values we found:
[tex]$$a_n = 60 \cdot \left(\frac{1}{5}\right)^{n-1}.$$[/tex]
This is the explicit rule for the given geometric sequence.
[tex]$$a_1 = 60.$$[/tex]
Next, we find the common ratio by dividing the second term by the first term. The second term is:
[tex]$$a_2 = 12.$$[/tex]
Thus, the common ratio is:
[tex]$$r = \frac{a_2}{a_1} = \frac{12}{60} = \frac{1}{5}.$$[/tex]
For any geometric sequence, the explicit formula for the [tex]$n$[/tex]th term is given by:
[tex]$$a_n = a_1 \cdot r^{n-1}.$$[/tex]
Substituting the values we found:
[tex]$$a_n = 60 \cdot \left(\frac{1}{5}\right)^{n-1}.$$[/tex]
This is the explicit rule for the given geometric sequence.