Mathematics: The sequence 5, 10, 20, 40 … shows the number of “likes” on a viral video each day starting with the day it was published. a) what is the recursive rule for the sequence? b) what is the explicit rule for the sequence?

y = 7Step-by-step explanation:...

The sequence 5, 10, 20, 40 … shows the number of

TheVariableWhoLived

10.03.2022

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 $a_n=a_1r^{n-1}$

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

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