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;

$\frac{\sum x}{n} =15$

$\Rightarrow \frac{x+(x+2)+(x+4)+(x+6)}{4} =15$

$\Rightarrow \frac{x+x+2+x+4+x+6}{4} =15$

$\Rightarrow \frac{x+x+x+x+2+4+6}{4} =15$

$\Rightarrow \frac{4x+12}{4} =15$

Multiply both sides by 4 to obtain,

$\Rightarrow 4\times \frac{4x+12}{4} =4 \times15$

$\Rightarrow 4x+12 =60$

$\Rightarrow 4x =60-12$

$\Rightarrow 4x =48$

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 $12$.