Question

calculate 1 - 2 + 3 - 4 + 5 - 6 +.......+179 - 180​

Answer 1

Step-by-step explanation:

1-2+3-4+5-6+7-8+...........+179-180

= (1+3+5+7+9....179) - (2+4+6+8+10.....180)

Addition of A.P sequence : (1+3+5......+179)

An = a + (n-1)d

179 = 1+(n-1)2

89+1 = n

n= 90

Sn = n/2 ( 2a+(n-1)d)

Sn = 90/2*(2(1)+(90-1)2)

Sn = 45*(180)

Sn = 45*180 = 8100

Addition of A.P sequence : (2+4+6+8.....+180)

An = a+(n-1)d

180 = 2 + (n-1)2

n = 90

then

Sn = 90/2*(2(2)+(90-1)2)

Sn = 45*(182)

then total addition = 45*180 - 45*182

= 45*(-2)

= -90