Answer:
a) [tex]a_n=2(a_{n-1})[/tex], where [tex]a_1=5[/tex].
b) [tex]a_n=5(2)^{n-1}[/tex]
Step-by-step explanation:
The given sequence is
[tex]5,10,20,40...[/tex].
The first term of the sequence is
[tex]a_1=5[/tex]
The second term is [tex]a_2=10[/tex]
The common ratio for this sequence can be determined using any two consecutive terms in the sequence.
Using the first two terms, the common ratio is
[tex]r=\frac{a_2}{a_1}[/tex]
[tex]\Rightarrow r=\frac{10}{5}=2[/tex]
a) The recursive rule is given by,
[tex]a_n=r(a_{n-1})[/tex]
[tex]a_n=2(a_{n-1})[/tex], where [tex]a_1=5[/tex].
b) The explicit rule is given by [tex]a_n=a_1r^{n-1}[/tex]
[tex]\Rightarrow a_n=5(2)^{n-1}[/tex]
