Question

Can you help me solve this? And step by step please?

Answer 1

The recursive formular for geometric sequence:

Recursive formula for a geometric sequence is

`a_n=a_(n-1)* r`

where r is the common ratio

`(1)/(2),(3)/(4),(9)/(8),(27)/(16)`
`\begin{gathered} r=(T_2)/(T_1)=(T_3)/(T_2) \\ r=(3)/(4)/(1)/(2)=(3)/(4)*(2)/(1)=(3)/(2) \\ r=(9)/(8)/(3)/(4)=(9)/(8)*(4)/(3)=(3)/(2) \end{gathered}`

This is called recursive formula for geometric sequence.

Hence the recursive formula =

`a_1=(1)/(2),a_n=a_(n-1)\text{.}((3)/(2))\text{ for }n\ge2`