Question

If the average of the first $n$ numbers in the sequence $148,146,144,.........$ is $125$, then $n=$

• A. $18$
• B. $24$
• C. $30$
• D. $36$

Answer 1

The correct option is B $24$

The given sequence is an A.P. with first term $a=148$ and common difference $d=-2$. The average of the first $n$ terms is given by

Average $=\frac{\text{Sum of first}n\text{terms}}{n}$

$\therefore \frac{\frac{n}{2}(2a+(n-1\left)d\right)}{n}=125$
$\Rightarrow \frac{2\left(148\right)+(n-1)(-2)}{2}=125$
$\Rightarrow 149-n=125$
$\Rightarrow n=24$