Question

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

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

Answer 1

The correct option is B

$5^{th}$

Explanation for the correct option:

Given that,

First term of a G.P. $a=5$

Common ratio $r=-5$

$n^{th}$ terms of a G.P. $t_n=3125$

We know that $t_n=a.r^{n-1}$

$\begin{array}{crcl}\Rightarrow & a.r^{n-1}& =& 3125\\ \Rightarrow & \left(5\right).{\left(-5\right)}^{n-1}& =& 3125\\ \Rightarrow & {\left(-5\right)}^{n-1}& =& \frac{3125}{5}\\ \Rightarrow & {\left(-5\right)}^{n-1}& =& 625\\ \Rightarrow & {\left(-5\right)}^{n-1}& =& {\left(-5\right)}^4\\ \Rightarrow & n-1& =& 4\\ \Rightarrow & n& =& 5\end{array}$

Therefore, $5^{th}$ term is $3125$

Hence, the correct answer is option (B) i.e. $5^{th}$