Answer:
recursive formula = [tex]a_{n} = a_{n-1}* r[/tex]
explicit formula: [tex]a_{n} = a_{1}*r^{n-1}[/tex]
Step-by-step explanation:
Thinking process:
Let a sequence be given as:
3 9 27 81
As can be observed from the sequence, the next number of the sequence is a multiple of 3, that is 9 is a multiple of 3. Similarly, 27 is 9 multiplied by 3
then, let the first term be a. the common multiplying factor will be r (in this case 3). Then the formula will be [tex]a_{n} = a_{n-1}*r[/tex]
In addition, the powers rule applies.
For instance:
9 = [tex]3^{2}[/tex]
27 = [tex]3^{3}[/tex]
81 = [tex]3^{4}[/tex]
Then the explicit formula will be [tex]a_{n} = a_{1}*r^{n-1}[/tex]
