Answer:
Explicit rule for this sequence is, [tex]a_n = 49\cdot (3)^{n-1}[/tex]
Step-by-step explanation:
A recursive rule for a geometric sequence is [tex]a_1=49[/tex], [tex]a_n = 3a_{n-1}[/tex]
First term [tex]a_1= 49[/tex]
To get second term, just multiply the first term by 3
[tex]a_n = 3 a_{n-1}[/tex]
[tex]a_2 = 3 a_1[/tex]
[tex]a_2= 3\cdot 49 [/tex]
so, we get the common ratio r = 3
Now, Explicit rule for geometric sequence is given by:
[tex]a_n = a_1 \cdot (r)^{n-1}[/tex]
Here, [tex]a_1= 49[/tex] and r= 3
So, explicit rule is :
[tex]a_n = 49\cdot (3)^{n-1}[/tex]
