Question

The sum of 3 consecutive even numbers is 78. What is the second number in this sequence?

Answer 1

`26`

Explanation:

If the number of a set of consecutive numbers is odd, the sum of the consecutive numbers is the number of consecutive numbers * the middle number.

Here, the sum is 78.

We can find the middle number, in this case, the 2nd, by diving 78 by 3.

`78/3 = 26`

The second number is 26.

Answer 2

`"second number "=26`

Explanation:

Since there is a `color(blue)" difference of 2"` between even numbers then.

We can generalise the sum of 3 consecutive even numbers as follows.

Let the 3 even numbers be : `n,n+2,n+4`

`rArrn+(n+2)+(n+4)=78larr" equation to be solved"`

`rArr3n+6=78`

subtract 6 from both sides.

`3ncancel(+6)cancel(-6)=78-6`

`rArr3n=72`

To solve for n, divide both sides by 3

`(cancel(3) n)/cancel(3)=72/3`

`rArrn=24larr" first even number"`

`n+2=24+2=26larrcolor(red)" second even number"`

`n+4=24+4=28larr" third even number"`

`"Check: " 24+26+28=78`