Question

If the ${10}^{th}$ term of a geometric progression is 9 and $4^{th}$ term is 4, then its $7^{th}$ term is

• A. $6$
• B. $36$
• C. $\frac{4}{9}$
• D. $\frac{9}{4}$

Answer 1

The correct option is A

$6$

Explanation for Correct option :

Step 1: Apply the G.P. formula

Let the first term and common ratio of the given G.P. be a and r respectively

The $n^{th}$ term$=a{r}^{n-1}$

${10}^{th}$ term, $a{r}^9=9$…(i)

$4^{th}$ term,$a{r}^3=4$…(ii)

Step 2:Multiply (i) and (ii)

$$\begin{gathered} \Rightarrow a{r}^{9}a{r}^3=36 \\ \Rightarrow a^2{r}^{12}=36 \\ \Rightarrow {\left(a{r}^6\right)}^2={\left(6\right)}^2 \end{gathered}$$

Taking Square root

$$\begin{gathered} \Rightarrow {\mathrm{ar}}^6=6 \\ \therefore 7^{\mathrm{th}}\mathrm{term}={\mathrm{ar}}^6=6 \end{gathered}$$

Hence Option (1) is correct