Question

The average of even integers from 2 to 100, inclusive is?

Answer 1

Answer:

51

Step-by-step explanation:

Average of even integers from 2 to 100 including 2 and 100 is given as:

Average = Sum of all Integers / Number of Integers

Sum of all integers = 2 + 4 + 6 + ... 100

⇒ It forms an A.P

• a = 2
• d = 2
• n = ?
• aₙ = 100

⇒ aₙ = a + ( n - 1 ) d

⇒ 100 = 2 + ( n - 1 ) 2

⇒ 100 - 2 = ( n - 1 ) 2

⇒ 98 = ( n - 1 ) 2

⇒ 98/2 = ( n - 1 )

⇒ 49 = n - 1

⇒ n = 49 + 1 = 50

Therefore number of integers is 50.

Sum = n/2 [ a + aₙ ]

⇒ Sum = 50/2 [ 2 + 100 ]

⇒ Sum = 25 [ 102 ]

⇒ Sum = 2550

Therefore Sum of all even integers from 2 to 100 is 2550

⇒ Average = Sum / Total number of integers

⇒ Average = 2550 / 50

⇒ Average = 51

Hence the average of even integers from 2 to 100 inclusive is 51.

Answer 2

Answer:-

A.P

a = 2

d = 2

• n = let us find

aₙ = 100

aₙ = a + ( n - 1 ) d

100 = 2 + ( n - 1 ) 2

100 - 2 = ( n - 1 ) 2

98 = ( n - 1 ) 2

98/2 = ( n - 1 )

49 = n - 1

n = 49 + 1 = 50

• So, 50 is the number of integers.

= n/2

= 50/2 *2 + 100

= 25 *102

= 2550

= 2550 / 50

= 51

Therefore, the average of even integers from 2 to 100 inclusive is 51