Question

If the sum of first 50 natural numbers is 1275 and the sum of first 50 odd numbers is 2500 then the sum of the first 50 even numbers is​

Answer 1

Solution:-

The even number is

=> 2 , 4 , 6 , 8 .............

=> a = 2

=> d = a₂ - a₁ = 4 - 2 = 2

=> n = 50

Sum of 50 term

$\rm \: formula \\ \boxed{\rm \: S_n = \frac{n}{2 } \{2a + (n - 1)d \}}$

Put the value on formula

$\rm \: S_{50} = \dfrac{50}{2} \{2 \times 2 + (50 - 1)2 \}$

$\rm \: = 25 \{4 + (49) \times 2 \}$

$= 25 \{4 + 98 \}$

$= 25 \{102 \}$

$= 2550$

So , the sum of first 50 even number = 2550

More information

Definition of AP

=> An arithmetic progression is a numerical sequence or series,

in which every consecutive value after the first is derived by adding a constant. This constant is called the common difference.

Such a numerical sequence is considered a progression because the last term in the sequence can be represented by an equation.

So in order to find out the sum of n terms in Arithmetic Progression,