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

ANSWER

$\begin{gathered} 1)5.695 \\ Nth\text{ term }\frac{1}{2}\times(\frac{3}{2})^{n-1} \end{gathered}$

EXPLANATION

1.

Given;

$\frac{1}{2},\frac{3}{4},\frac{9}{8}$

Recall;

$T_n=a\times r^{n-1}$

Coommon ratio

$\begin{gathered} r=\frac{T_2}{T_1} \\ =\frac{3}{4}\div\frac{1}{2} \\ =\frac{3}{4}\times\frac{2}{1} \\ =\frac{2}{3} \end{gathered}$

Hence;

$\begin{gathered} a=\frac{1}{2},r=\frac{3}{2} \\ \end{gathered}$

Substituting the values;

$\begin{gathered} T_{n}=ar^{n-1} \\ =\frac{1}{2}\times(\frac{3}{2})^{7-1} \\ =0.5\times1.5^6 \\ =11.39\times0.5 \\ =5.695 \end{gathered}$

Nth term;

$\begin{gathered} T_n=\frac{1}{2}\times(\frac{3}{2})^{n-1} \\ \end{gathered}$