Answer:
[tex][/tex] The recursive formula for a geometric sequence is:
a_n = a_n-1 [tex] \times[/tex] r
where:
• a_n is the nth term in the sequence
• a_n-1 is the (n-1)th term in the sequence
• r is the common ratio between each term
To find the common ratio, we can divide any term by the previous term. For example:
r = [tex]\frac{a_2}{a_1}[/tex] = [tex]\frac{14}{2}[/tex] = 7
Therefore, the recursive formula for the given sequence is:
a_n = a_n-1 [tex] \times[/tex] 7
To find a_5, we can substitute n = 5 into the recursive formula and evaluate it:
```
a_5 = a_4 [tex] \times[/tex] 7
a_4 = a_3 [tex] \times[/tex] 7
a_3 = a_2 [tex] \times[/tex] 7
a_2 = a_1 [tex] \times[/tex] 7
```
Substituting these equations into each other, we get:
a_5 = a_1 [tex] \times[/tex] 7⁵
Since the first term in the sequence is 2, we have:
a_5 = 2 [tex] \times[/tex] 7⁵ = 33,614
Therefore, the answer is B) a_n = a_n-1 [tex] \times[/tex] 7; 33,614.
