Average
MCQs Math


Question:     Find the average of the first 2888 even numbers.


Correct Answer  2889

Solution And Explanation

Explanation

Method to find the average

Step : (1) Find the sum of given numbers

Step: (2) Divide the sum of given number by the number of numbers. This will give the average of the given numbers

The first 2888 even numbers are

2, 4, 6, 8, . . . . 2888 th terms

Calculation of the sum of the first 2888 even numbers

We can find the sum of the first 2888 even numbers by simply adding them, but this is a bit difficult. And if the list is long, it is very difficult to find their sum. So, in such a situation, we will use a formula to find the sum of given numbers that form a particular pattern.

Here, the list of the first 2888 even numbers forms an Arithmetic series

In an Arithmetic Series, the common difference is the same. This means the difference between two consecutive terms are same in an Arithmetic Series.

The sum of n terms of an Arithmetic Series

Sn = n/2 [2a + (n – 1) d]

Where, n = number of terms, a = first term, and d = common difference

In the series of the first 2888 even number,

n = 2888, a = 2, and d = 2

Thus, sum of the first 2888 even numbers

S2888 = 2888/2 [2 × 2 + (2888 – 1) 2]

= 2888/2 [4 + 2887 × 2]

= 2888/2 [4 + 5774]

= 2888/2 × 5778

= 2888/2 × 5778 2889

= 2888 × 2889 = 8343432

⇒ The sum of the first 2888 even numbers (S2888) = 8343432

Shortcut Method to find the sum of the first n even numbers

Thus, the sum of the first n even numbers = n2 + n

Thus, the sum of the first 2888 even numbers

= 28882 + 2888

= 8340544 + 2888 = 8343432

⇒ The sum of the first 2888 even numbers = 8343432

Calculation of the Average of the first 2888 even numbers

Formula to find the Average

Average = Sum of the given numbers/Number of the numbers

Thus, The average of the first 2888 even numbers

= Sum of the first 2888 even numbers/2888

= 8343432/2888 = 2889

Thus, the average of the first 2888 even numbers = 2889 Answer

Shortcut Trick to find the Average of the first n even numbers

(1) The average of the first 2 even numbers

= 2 + 4/2

= 6/2 = 3

Thus, the average of the first 2 even numbers = 3

(2) The average of the first 3 even numbers

= 2 + 4 + 6/3

= 12/3 = 4

Thus, the average of the first 3 even numbers = 4

(3) The average of the first 4 even numbers

= 2 + 4 + 6 + 8/4

= 20/4 = 5

Thus, the average of the first 4 even numbers = 5

(4) The average of the first 5 even numbers

= 2 + 4 + 6 + 8 + 10/5

= 30/5 = 6

Thus, the average of the first 5 even numbers = 6

Thus, the Average of the First n even numbers = n + 1

Thus, the average of the first 2888 even numbers = 2888 + 1 = 2889

Thus, the average of the first 2888 even numbers = 2889 Answer


Similar Questions

(1) Find the average of the first 4186 even numbers.

(2) Find the average of the first 4885 even numbers.

(3) What is the average of the first 136 even numbers?

(4) Find the average of the first 585 odd numbers.

(5) Find the average of even numbers from 12 to 96

(6) What is the average of the first 1336 even numbers?

(7) What will be the average of the first 4043 odd numbers?

(8) Find the average of the first 2824 even numbers.

(9) Find the average of odd numbers from 7 to 95

(10) Find the average of odd numbers from 15 to 1535


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