Question

The sum of 5 consecutive integers is 505. What is the third number in this sequence?

Answer 1

Answer:

The answer is 101. you can look at the other answers for a step by step solution.

Step-by-step explanation:

Answer 2

Final Answer:

The third number in this sequence is 101, where the sum of 5 consecutive integers is 505.

Given:

The sum of 5 consecutive integers is 505.

To Find:

The third number in this sequence, where the sum of 5 consecutive integers is 505.

Explanation:

Note the following for the solution to the present problem.

The five consecutive integers can be any of those sequential integers that differ by one from the consecutive numbers.

Step 1 of 3

Assume the five consecutive integers are $n,(n+1),(n+3),(n+4),(n+5)$

Step 2 of 3

Form the following equation from the fact that the sum of 5 consecutive integers is 505, and solve it.

$n+(n+1)+(n+2)+(n+3)+(n+4)=505\\5n+(1+2+3+4)=505\\5n+10=505\\5n=495\\n=\frac{495}{5} \\n=99$

Step 3 of 3

The third number in this sequence, where the sum of 5 consecutive integers is 505, is

$=(n+2)_{n=99}\\=99+2\\=101$

Therefore, the required third number in this sequence is 101, where the sum of 5 consecutive integers is 505.

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