Question

The sum of five consecutive odd numbers is $575$. What is the sum of the next set of the consecutive odd numbers?

• A. $625$
• B. $615$
• C. $635$
• D. Cannot be determined
• E. None of these

Answer 1

The correct option is A $625$

Let the first five consecutive odd numbers be $x,x+2,x+4,x+6,x+8$.

Now, it is given that the sum of first five consecutive odd numbers is $575$ which means:

$x+(x+2)+(x+4)+(x+6)+(x+8)=575\Rightarrow 5x+20=575\Rightarrow 5x=575-20\Rightarrow 5x=555\Rightarrow x=\frac{555}{5}$

Therefore, the first odd integer is $111$ then the second integer is $x+2=111+2=113$, the third integer is $x+4=111+4=115$, the forth integer is $x+6=111+6=117$ and the fifth integer is $x+8=111+8=119$

The set of first five consecutive odd numbers is $111,113,115,117,119$. Similarly, the set of next five consecutive odd numbers will be $121,123,125,127,129$ and their sum can be determined as follows:

$121+123+125+127+129=625$

Hence, the sum of next set of consecutive odd numbers is $625$.