Question

The sum of six consecutive numbers is $150$. Find the first number

• A. $20.1$
• B. $22.5$
• C. $20.5$
• D. $21.5$

Answer 1

Answer: (B)

$22.5$

$5$ consecutive numbers form an arithmetic progression with difference $1$.
$n=6,s_6=150,d=1$
Using the formula, $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
Therefore, $150=\frac{6}{2}[2a+(6-1\left)1\right]$
$\Rightarrow 150=3[2a+5]$

$\Rightarrow a=\frac{45}{2}=22.5$
Thus the first number is $22.5$.