If thew first and sixth terms of geometric progessions are $$\frac{2}{3}$$ and 162 respectively then the $$8^{th}$$ term of the progression is
let the first term is a and common ratio is r then
$$T_{1}$$= {a}$$\times{r}^{1-1}$$ = a =Â Â $$\frac{2}{3}$$Â Â Â Â Â Â Â Â Â equation 1
$$T_{6}$$= {a}$$\times{r}^{6-1}$$ =Â {a}$$\times{r}^{5}$$ = 162Â Â Â Â equation 2
equation 1 \equation 2
$$\frac{2}{3}$$\162 = 1\r^5
243 = r^5
3 = r
r = 3Â
put the value of a and r in equation following equationÂ
$$T_{8}$$= {a}$$\times{r}^{8-1}$$ =Â $$\frac{2}{3}$$Â $$\times{3}^{7}$$Â
               $$T_{8}$$     =  $$\frac{2}{3}$$ $$\times243$$ $$\times3$$ $$\times3$$                 Â
               $$T_{8}$$    = 1458   AnswerÂ
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