Math, asked by srijitasen25, 16 days ago

calculate 1-2+3-4+5-6………....+179-180​

Answers

Answered by dylansweeney
0

Answer:

This can be split into two Arithmetic progressions:

1+3+5...+179  and -2-4-6...-180

Now, we will find sum of them separately using summation formula of AP

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

where = sum of n terms

d = common difference

a = first term of AP

First, we will no of terms i.e. n of both APs

a) 1+3+5...+179 179 = a+(n-1)d

179 = 1+(n-1)2

179-1 = (n-1)2

178/2 = n-1

89+1 = n

n= 90

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

                         = 90/2{2*1 +(90-1)2}                        

                         = 45{2+89*2}                        

                         =45{2+178}

                        = 45*180 = 8100

b) -2-4-6...-180 = -(2+4+6...+180)

180 = a+(n-1)d

180 = 2+(n-1)2

180-2 = (n-1)2

178/2 = n-1

89+1 = n

n= 90

(b)= n/2{2a+(n-1)d}

                         = 90/2{2*2 +(90-1)2}

                         = 45{4+89*2}

                         =45{4+178}

                         = 45*182

                         = 8190

Now, 1+3+5...+179-2-4-6...-180      

+= 8100 - 8190  = -90

Answer is -90

Step-by-step explanation:

Answered by preetisinghallavanya
0

Answer:

correct answer is -90

Step-by-step explanation:

hope it helps

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