Question

the mean of four consecutive even numbers is 15.the greatest of these numbers is a1.the least of these numbers is a2.

Answer 1

Hello,

I suppose you want the 4 numbers.

Let's call the numbers
`2n,2n+2,2n+4,2n+6`

`2n+2n+2+2n+4+2n+6[=8n+12=15*4\\ 8n+12=60\\ 8n=48\\ n=6\\\\ 2n=12\\ 2n+2=14\\ 2n+4=16\\ 2n+6=18\\`

Answer 2

Let x be the first even number. Then adding 2 consecutively gives us the subsequent even numbers. That is

`x,x+2,x+4,x+6`

From the question, the mean of these four numbers is 15. That is;

`(\sum x)/(n) =15`

`\Rightarrow (x+(x+2)+(x+4)+(x+6))/(4) =15`

`\Rightarrow (x+x+2+x+4+x+6)/(4) =15`

`\Rightarrow (x+x+x+x+2+4+6)/(4) =15`

`\Rightarrow (4x+12)/(4) =15`

Multiply both sides by 4 to obtain,

`\Rightarrow 4* (4x+12)/(4) =4 *15`

`\Rightarrow 4x+12 =60`

`\Rightarrow 4x =60-12`

`\Rightarrow 4x =48`

Divide both sides by 4 to obtain,

`x =12`

Hence the greatest of the numbers is
`12+6=18`

and the least of the numbers is
`12`.