Question

Find an explicit and a recursive formula for each geometric sequence:
16,4,1,1/4,1/16
Explicit formula
Recursive formula

5,15,45,135,405
Explicit formula
Recursive formula

Answer 1

1)
\(\Large \color{MidnightBlue}{\Rightarrow 64 \div 4^n }\)
\(\Large \color{MidnightBlue}{\Rightarrow 16 \div 4^{n - 1} }\)

Can you tell which is explicit and which is recursive?

Answer 2

Explicit: \(T_n = a_1 \times r^{n-1} \)
Recursive: \(T_1= 16\) and \( \forall n >1,\in \mathbb{N} ,\;\; T_{n+1} = T_n\times r\)

Answer 3

\(a_1 =\) First term
\(T_n =\) nth term
\(r=\) common ratio