Question

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Q38. If the average of first 'n' consecutive even numbers is multiplied by four and then the resultant is divided by 20 gives result 5. What is the value of n?
1
(A) 24
(B) 20
(C) 25
(D) 40
​

Answer 1

If the average is n

then, n×4/20=5

i.e.n/5=5

Thus, n=5×5=25

Thus, n=25

Answer 2

The value of n = 24

Given :

The average of first 'n' consecutive even numbers is multiplied by four and then the resultant is divided by 20 gives result 5

To find :

The value of n is

(A) 24

(B) 20

(C) 25

(D) 40

Solution :

Step 1 of 2 :

Form the equation to find the value of n

The sum of first n consecutive even numbers = n(n + 1)

∴ Average of first n consecutive even numbers

$\displaystyle \sf = \frac{n(n + 1)}{n}$

$\displaystyle \sf{ } = n + 1$

By the given condition

$\displaystyle \sf \frac{4(n + 1)}{20} = 5$

Step 2 of 2 :

Find the value of n

$\displaystyle \sf \frac{4(n + 1)}{20} = 5$

$\displaystyle \sf \implies \frac{(n + 1)}{5} = 5$

$\displaystyle \sf{ \implies }n + 1 = 25$

$\displaystyle \sf{ \implies }n = 25 - 1$

$\displaystyle \sf{ \implies }n = 24$

∴ The value of n is 24

Hence the correct option is (A) 24

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