Question

determine the sum :1+(-2)+3+(-4)+5+(-6)+....+(-50).​

Answer 1

Answer:

-25

Step-by-step explanation:

Given :

To find th value of :

1 - 2 + 3 - 4 + 5 - 6 .... - 50

Solution :

By using pure logic :

⇒ 1 - 2 + 3 - 4 + 5 - 6 .... - 50   ( 50 terms)

⇒ (1 - 2) + (3 - 4) + (5 - 6) ....+ (49 - 50)  ( 25 terms)

⇒ (-1) + (-1) + (-1) + (-1) + .... + (-1)   (25 terms)

⇒ -1 × 25 = -25

___

By using formula,

⇒ 1 - 2 + 3 - 4 + 5 - 6 .... - 50

⇒ ( 1 + 3 + 5 + 7 + ... + 49 ) - ( 2 + 4 + 6 + 8 + ... + 50 )

We know that,

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

Applying here,

$a = 1$ , $a' = 2$

$n = 25$

$d = 2$

⇒ ( 1 + 3 + 5 + 7 + ... + 49 ) - ( 2 + 4 + 6 + 8 + ... + 50 )

⇒ $\frac{25}{2}(2(1) + (25 -1)2) - \frac{25}{2} (2(2) + (25 - 1)2)$

⇒ $\frac{25}{2} (2 + (24)2) - \frac{25}{2} (4 + (24)2)$

⇒ $\frac{25}{2} (2 + 48) - \frac{25}{2} (4 + 48)$

⇒ $\frac{25}{2} (50) - \frac{25}{2} (52)$

⇒ $\frac{25}{2} (50 - 52)$

⇒ $\frac{25}{2} (-2) = \frac{-50}{2} = -25$

Answer 2

Answer:

-25

Step-by-step explanation:

There are 25 pairs.

Each pair answer is -1.

25*-1= -25

Thanks.