Question

If the first term of a G.P. is 5 and the common ratio is -5, then 3125 is the ____ term.

• A. $6^{th}$
• B. $5^{th}$
• C. $7^{th}$
• D. $8^{th}$

Answer 1

The correct option is B

$5^{th}$

Given that the first term $a=5$ and common ratio $r=-5.$

Suppose that $n^{th}$ term is 3125.

Then, $a_n=a{r}^{n-1}=3125.$
$\Rightarrow 5(-5{)}^{n-1}=3125$
$\Rightarrow (-5{)}^{n-1}=\frac{3125}{4}=625=5^4$
i.e., $(-1{)}^{n-1}\times 5^{n-1}=5^4$
Since $\frac{5^4}{5^{n-1}}>0,$ we have $(-1{)}^{n-1}=1.$
Thus, $5^{n-1}=5^4.$
$\Rightarrow n=5$