Answer:
[tex]\boxed{ a_{n} = 6a_{n-1}}[/tex]
Step-by-step explanation:
Step 1. Determine the common ratio
The formula for the nth term of a geometric sequence is
aₙ = a₁rⁿ⁻¹
Data:
a₁ = 4
n = 6
a₆ =31 104
Calculation:
31 104 = 4r⁵
r⁵ = 7776
[tex]r = \sqrt [5]{7776}[/tex]
r = 6
aₙ = 4(6)ⁿ
Step 2. Determine the recursive formula.
aₙ = 4(6)ⁿ
aₙ₋₁ = 4(6)ⁿ⁻¹
[tex]\dfrac{a_{n}}{{a_{n-1}}} = \dfrac{4(6)^{n} }{4(6)^{n-1}} = 6\\\\a_{n} = 6a_{n-1}[/tex]
The recursive formula for the series is [tex]\boxed{ a_{n} = 6a_{n-1}}[/tex]
