Questions & Answers

Question

Answers

A. 625

B. 615

C. 635

D. Cannot be determined

E. None of these

Answer
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 .

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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