Question

PLLLZ HELP Write a recursive formula for finding the nth term of each geometric sequence.
5, 20, 80, ...

a1 = 20, an = 4an − 1

a1 = 80, an = 4an − 1

a1 = 5, an = 4an − 2

a1 = 5, an = 4an − 1

Answer 1

Answer:

$a_1 = 5,\\a_n =4 a_{n-1}$

Step-by-step explanation:

The first term of the geometric sequence is

$a_1 =5$.

The common ratio between the consecutive terms is

$\dfrac{20}{5} = 4,$

$\dfrac{80}{20} = 4;$

therefore, we see that the nth term is found by

$a_n =4 a_{n-1}$

Thus, the recursive formula for the geometric sequence is

$a_1 = 5,\\a_n =4 a_{n-1}.$