Question

What is the explicit rule for the nth term of the geometric sequence? 5, 20, 80, 320, 1,280, … an = 5(4n 1) an = 5(4n – 1) an = 4(5n – 1) an = 5(4n)

Answer 1

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

Step-by-step explanation:

the nth term ( explicit rule ) of a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

a₁ is the first term , r the common ratio , n the term number

here a₁ = 5 and r =
`(a_(2) )/(a_(1) )` =
`(20)/(5)` = 4 , then explicit formula is

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

Answer 2

The explicit rule for the nth term of the given geometric sequence is an = 5(4^(n-1)), with a common ratio of 4 and the first term being 5.

Step-by-step explanation:

To determine the explicit rule for the nth term of the geometric sequence provided (5, 20, 80, 320, 1280, ...), we first need to identify the common ratio. The common ratio (r) is the factor by which we multiply one term to get the next term. In this sequence, multiplying a term by 4 gives us the subsequent term (for example, 5 * 4 = 20, 20 * 4 = 80, and so on).

The nth term of a geometric sequence is found using the formula an = a1 * r^(n-1), where a1 is the first term and n is the term number.

For our sequence, the first term a1 is 5 and the common ratio r is 4. Applying the formula, the nth term an is 5 * 4^(n-1). Therefore, the explicit rule for the nth term is an = 5(4^(n-1)).