Question

Seven consecutive integers are added. The sum is 6 times the greatest of the seven integers .what is the smallest integer

Answer 1

the smallest integer is 15

note that consecutive integers have a difference of 1 between them

let the smallest integer be n

then : n, n+ 1, n + 2, n + 3, n + 4, n + 5, n + 6

are seven consecutive integers with n + 6 being the largest, thus summing gives

7n + 21 = 6(6 + n)

7n + 21 = 36 + 6n ( distributing right side )

7n - 6n + 21 = 36 ( subtracting 6n from both sides )

n + 21 = 36 ⇒ n = 36 - 21 = 15

the smallest integer is 15

Answer 2

The smallest integer is 15.

What are Integers ?

A whole number that can be positive , negative and zero but not a fraction is called an Integer.

It is given in the question that seven consecutive integers are added.

The sum is 6 times the greatest of the seven integers

Let the first integer be x

Then the integers will be

x , x+1 , x+2 ,x+3 ,x +4, x+5, x+6

From the question

x +x+1 +x+2 +x+3 +x +4+ x+5+ x+6 = 6(x+6)

7x +21= 6x +36

x = 15

The smallest integer is 15.

To know more about Integers

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