Question

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Answer 1

Answer:

a) $a_n=2(a_{n-1})$, where $a_1=5$.

b)  $a_n=5(2)^{n-1}$

Step-by-step explanation:

The given sequence is

$5,10,20,40...$.

The first term of the sequence is

$a_1=5$

The second term is $a_2=10$

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

$r=\frac{a_2}{a_1}$

$\Rightarrow r=\frac{10}{5}=2$

a) The recursive rule is given by,

$a_n=r(a_{n-1})$

$a_n=2(a_{n-1})$, where $a_1=5$.

b) The explicit rule is given by $a_n=a_1r^{n-1}$

$\Rightarrow a_n=5(2)^{n-1}$