# Test: Geometric Series I - Ambitious

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Question 1:   Express the term of a geometric progression $\text{\hspace{0.17em}}{a}_{18}\text{\hspace{0.17em}}$ through its another term $\text{\hspace{0.17em}}{a}_{12}\text{\hspace{0.17em}}$ and its common ratio $\text{\hspace{0.17em}}r\text{\hspace{0.17em}}$ .
${a}_{18}=\frac{{a}_{12}}{{r}^{6}}$
${a}_{18}={a}_{12}×6r$
${a}_{18}={a}_{12}+6r$
${a}_{18}={a}_{12}×{r}^{6}$
Question 2:   ($\text{\hspace{0.17em}}{a}_{n}\text{\hspace{0.17em}}$ ) is a geometric sequence. Put the sign between these two expressions: .
Question 3:   Find the initial term of the geometric sequence ($\text{\hspace{0.17em}}{a}_{n}\text{\hspace{0.17em}}$ ), if $\text{\hspace{0.17em}}r=\frac{1}{2}\text{\hspace{0.17em}}$ , $\text{\hspace{0.17em}}{a}_{4}=\frac{1}{32}\text{\hspace{0.17em}}$ .
$\frac{1}{4}$
$4$
$\frac{1}{2}$
$\frac{1}{8}$
Question 4:   $192\text{\hspace{0.17em}}$ is a term of a geometric sequence: . Find its number.
$7$
$6$
$5$
$10$
Question 5:   What two numbers should be put between $\text{\hspace{0.17em}}3\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}192\text{\hspace{0.17em}}$ two create a geometric progression?
$12;\text{\hspace{0.17em}}48$
$-12;\text{\hspace{0.17em}}48$
$52;\text{\hspace{0.17em}}103$
$66;\text{\hspace{0.17em}}129$
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