Question

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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?

Answer 1

a)
`a_n=2(a_(n-1))`, where
`a_1=5`.

b)
`a_n=5(2)^(n-1)`

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=(a_2)/(a_1)`

`\Rightarrow r=(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)`