Question

sum of first 25 even numbers? by progressions

Answer 1

Hey friend..!!! here's your answer
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First , We make an A.P of 1 to 25 even number .

2 , 4 , 6 ..............., 50

a = 2
d = a2 - a1
d= 4 - 2
d = 2
an = 50
n = 25

By using Sn Formula ===>

$sn = \frac{n}{2}(a +l)$
n = 24
a = 2
l = 50

$\frac{25}{2} (2 + 50) = \frac{25}{2} \times 52 \\ 25 \times 26 \\ =650$

So the Sum of 1 to 25 even number is 650

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#Hope its help you dear#
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Answer 2

Sol : The A.P. formed by first 25 even numbers is like this 2,4,6,8..........,50.

First term ( a ) = 2

Common term ( d )= 4 - 2 = 2.

Number of terms ( n ) = 25.

Sum of n terms = n/2{ 2 a + ( n - 1 ) d }


Sum of 25 terms = 25 / 2 { 2 x 2 + ( 25 - 1 ) 2 }

Sum of 25 terms = 25 / 2 { 4 + ( 2 4 ) 2 }

Sum of 25 terms = 25 / 2 ( 4 + 48 )

 Sum of 25 terms = ( 25 / 2 ) x 52

Sum of 25 terms =  ( 25 x 52 ) / 2

Sum of 25 terms = 1,300 / 2

Sum of 25 terms = 650.

So, the sum of first 25 even numbers is 650.