Question

What is the explict formula for this sequence 5, 10, 20, 40, 80, 160, ...

Answer 1

`a_(n)` = 5
`(2)^(n-1)`

Explanation:

there is a common ratio between consecutive terms , that is

10 ÷ 5 = 20 ÷ 10 = 40 ÷ 20 = 80 ÷ 40 = 2

this indicates the sequence is geometric with explicit formula

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

here a₁ = 5 and r = 2 , then

`a_(n)` = 5
`(2)^(n-1)`

Answer 2

Explanation:

as we see in the sequence, each term is twice of the previous term.

we mark the Nth as a(N), then:

a(N)=2a(N-1)