Question

The average of four consecutive even numbers is X. If the next two consecutive aven numbers are
included, what will be the new average?​

Answer 1

SOLUTION :-

GIVEN :-

• The average of four consecutive even numbers is X.
• The next two consecutive even numbers are included

TO DETERMINE :-

The new average

EVALUATION :-

Let four consecutive even numbers are

n, n + 2, n + 4, n + 6

Here it is given that the average of four consecutive even numbers is X

$\displaystyle \sf{X = \frac{n + (n + 2 )+ (n + 4) +( n + 6)}{4} \: }$

$\implies \displaystyle \sf{4X = n + (n + 2 )+ (n + 4) +( n + 6) }$

$\implies \displaystyle \sf{4X = 4 n +12}$

$\implies \displaystyle \sf{X = n +3}$

$\implies \displaystyle \sf{n = X - 3}$

Now the next two consecutive even numbers are included i.e n + 8 & n + 10 are added

So the new sum of 6 numbers are

$= \sf{n + (n + 2 )+ (n + 4) +( n + 6) + (n + 8) + (n + 10)}$

$= \sf{6n + 30}$

$= \sf{6(n + 5)}$

Hence the new average

$\displaystyle \sf{ = \frac{6(n + 5)}{6} }$

$= \sf{n + 5 \: }$

$\displaystyle \sf{ = X - 3 + 5}$

$\displaystyle \sf{ = X + 2}$

FINAL ANSWER :-

Hence the new average = X + 2

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Answer 2

Answer:

it will increase by 2

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