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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 Verified Verified
Hint-Proceed these types of questions by taking x as the first odd number and adding 2 in every consecutive term. Add the terms and evaluate with what is given in the question to find x . Once x is found we can find all the consecutive odd numbers along with the next set .

Complete step-by-step answer:
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:
$ \Rightarrow $ x+(x+2)+(x+4)+(x+6)+(x+8)=575
$ \Rightarrow $5x+20=575
$ \Rightarrow $5x=575−20
$ \Rightarrow $5x=555
$ \Rightarrow x = \dfrac{{555}}{5} = 111$
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:
$ \Rightarrow $121+123+125+127+129=625
Hence, the sum of the next set of consecutive odd numbers is 625.

Note-In this particular type of question always add 2 in the next consecutive number even if the consecutive numbers are even . Most of the students find it difficult to understand the concept working behind the question . It does not matter whether the numbers are odd or even as the sum does not depend on it . Also keep in mind to start the new set after the first set of numbers is completed .
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