Find: The 12^ th term of the G.P. 1 a^3x^3 ,ax,a^5x^5 - Vidyadip

Question

Find:
The $12^{th}$ term of the G.P. $\frac{1}{\text{a}^3\text{x}^3},\text{ax},\text{a}^5\text{x}^5\dots$

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Answer

$12^{th}$ term of the G.P. $\frac{1}{\text{a}^3\text{x}^3},\text{ax},\text{a}^5\text{x}^5\dots$
$\text{a}=\frac{1}{\text{a}^3\text{x}^3}$
$\text{r}=\frac{\text{t}_\text{n}}{\text{t}_{\text{n}-1}}=\frac{\text{t}_2}{\text{t}_1}=\frac{\text{a}\text{x}}{\frac{1}{\text{a}^3\text{x}^3}}=\text{a}^4\text{x}^4$
$\text{t}_\text{n}=\text{ar}^{\text{n}-1}$
$\text{t}_{12}=\text{ar}^{11}$
$=\Big(\frac{1}{\text{a}^3\text{x}^3}\Big)\big(\text{a}^4\text{x}^4\big)^{11}$
$=(\text{a}\text{x})^{41}$

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