Question

the sum of the 1st and 4th consecutive even numbers is 12 more than the difference between the 2nd and 3rd consecutive even numbers. find these 4 consecutive even numbers

Answer 1

Answer:

☢ Even Number : Any integer (never a fraction) that can be divided exactly by 2.

⠀

As these Four Even Numbers Should be Consecutive, So let's Number be a, (a + 2), (a + 4), (a + 6).

⠀

• First Even No : a
• Second Even No : (a + 2)
• Third Even No : (a + 4)
• Fourth Even No : (a + 6)

$\rule{100}{0.8}$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf (Even_1+Even_4)=(Even_3-Even_2)+12\\\\\\:\implies\sf a + (a + 6) = (a + 4) - (a + 2) + 12\\\\\\:\implies\sf a + a + 6 = \bcancel{a}+ 4 - \bcancel{a} - 2 + 12\\\\\\:\implies\sf 2a + 6 = 4 - 2 + 12\\\\\\:\implies\sf 2a + 6 = 14\\\\\\:\implies\sf 2a = 14 - 6\\\\\\:\implies\sf 2a = 8\\\\\\:\implies\sf a = \dfrac{8}{2}\\\\\\:\implies\sf a = 4$

$\rule{170}{1.5}$

☯ $\underline{\boldsymbol{Four\: consecutive \:Even\: Numbers :}}$

$\bullet\:\:\textsf{Even _\text1 = a = \textbf{4}}\\\bullet\:\:\textsf{Even _\text2 = (a + 2) = (4 + 2) = \textbf{6}}\\\bullet\:\:\textsf{Even _\text3 = (a + 4) = (4 + 4) = \textbf{8}}\\\bullet\:\:\textsf{Even _\text4 = (a + 6) = (4 + 6) = \textbf{10}}$

Answer 2

Given:-

• the sum of the 1st and 4th consecutive even numbers is 12 more than the difference between the 2nd and 3rd consecutive even numbers.

To find:-

• find these 4 consecutive even numbers.

Solution:-

★ Even Number:-

• A number which is divisible by 2 and generates a remainder of 0 is called an even number.

✦ Let's assume the four consecutive even number be a, (a + 2), (a + 4), (a + 6).

• First even number:- a

• Second even number:- (a + 2)

• Third even number:- (a + 4)

• Fourth even number:- (a + 6)

Now,

✦ According to given statement:-

$\bold{\underline{\boxed{\sf{\dag \; ( \sf Even_1 + \sf Even_4 ) = ( \sf Even_3 - \sf Even_2 ) + 12}}}}$

$\implies \sf{a + (a + 6) = (a + 4) - (a + 2) + 12}$

$\implies \sf{a + a + 6 = \cancel{a} + 4 - \cancel{a} - 2 + 12}$

$\implies \sf{2a + 6 = 4 - 2 + 12}$

$\implies \sf{2a + 6 = 14}$

$\implies \sf{2a = 14 - 6}$

$\implies \sf{2a = 8}$

$\implies \sf{a = \cancel{ \dfrac{8}{2}}}$

$\implies {\underline{\boxed{\sf{a = 4}}}}$

★ Therefore, The required consecutive Even Number :-

$\bullet \; \sf{ \sf Even_1 = a = 4}$

$\bullet \; \sf{ \sf Even_2 = (a + 2) = (4 + 2) = 6}$

$\bullet \; \sf{ \sf Even_3 = (a + 4) = (4 + 4) = 8}$

$\bullet \; \sf{ \sf Even_4 = (a + 6) = (4 + 6) = 10}$

$\rule{200}{2}$