Question

In each of the following geometric sequences, find (i) the 7th term; (i) the nth term.13 92. 7. 4 gb. V2, 2,2/2,13C.2.98

Answer 1

`\begin{gathered} 1)5.695 \\ Nth\text{ term }(1)/(2)*((3)/(2))^(n-1) \end{gathered}`

Step-by-step explanation

1.

Given;

`(1)/(2),(3)/(4),(9)/(8)`

Recall;

`T_n=a* r^(n-1)`

Coommon ratio

`\begin{gathered} r=(T_2)/(T_1) \\ =(3)/(4)/(1)/(2) \\ =(3)/(4)*(2)/(1) \\ =(2)/(3) \end{gathered}`

Hence;

`\begin{gathered} a=(1)/(2),r=(3)/(2) \\ \end{gathered}`

Substituting the values;

`\begin{gathered} T_(n)=ar^(n-1) \\ =(1)/(2)*((3)/(2))^(7-1) \\ =0.5*1.5^6 \\ =11.39*0.5 \\ =5.695 \end{gathered}`

Nth term;

`\begin{gathered} T_n=(1)/(2)*((3)/(2))^(n-1) \\ \end{gathered}`