Latest TCS Aptitude Question SOLUTION: What is the average of the first 200 terms of the series 1, -2, 3, -4, 5, -6, 7 …………

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What is the average of the first 200 terms of the series
1, -2, 3, -4, 5, -6, 7 …………

Asked In TCS vishnu (7 years ago)

Unsolved Read Solution (9)

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Read Solution (9) :

Prabhat Gupta  (7 years ago)

(1-2) + (3-4) + ...... 100 times

(-1) + (-1) + (-1) + ....100 times

average = (-100) / 200 = -1/2

Is this solution Helpfull? Yes (23) | No   

Abhishek  (7 years ago)

we can write
1+3+5+7+9+11+13.........+199 i.e 100 terms and
sum of n odd natural numbers is n^2 i.e 100^2 =10,000

-(2+4+6+8+10+12...........+200) i.e 100 terms and
sum of n even natural numbers is n(n+1) i.e -(100(100+1))= -10,100
average of first 200 terms = (10,000+(-10,100))/200
=-100/200
=-1/2 Ans.

Is this solution Helpfull? Yes (3) | No (1)  

soumya  (7 years ago)

(1-2+3-4...........-200)/200=(-100/200)=(-1/2)

Is this solution Helpfull? Yes (2) | No   

Shashank  (7 years ago)

(1-2)/2+(3-4)/2+....... 100 terms
=-1/2+(-1/2)+.....100 terms
=-50

Is this solution Helpfull? Yes (1) | No (5)  

nilesh gohil  (7 years ago)

1,-2,3,-4,5,-6,7,-8,9,-10

Is this solution Helpfull? Yes (1) | No (1)  

K Sai Likhith  (7 years ago)

sum of 100 odd numbers till 1-199=10000
sum of 100 even numbers till 2-200=10100
now subtact 2 from 1,we get -100;
so avg=-100/200=-0.5

Is this solution Helpfull? Yes (1) | No   

jayavelu  (7 years ago)

first find the sum of all (-)ve numbers i.e -2, -3, -4, -5,-6,-7, .............. -200
there are totally 199 terms therefore n=199.
so we get a1= -2, d=-1, an=-200.
now sn= n(a1+an)/2 i.e sn = 199(-202)/2
=-199(101) = -20099
now add positive nuber to it so total is -20099=1 = 20098

to get avg divide it by 200 so therefore 20098/200 = -100.49

now the average of the given term is -100.49

Is this solution Helpfull? Yes | No (5)  

Akhilakaithoj  (7 years ago)

-100/200 = -1/2

Is this solution Helpfull? Yes | No   

Saagnik Adhikary  (5 years ago)

The series consists of odd and even terms as 1, 3, 5, ..., 99 and -2, -4, -6, ...., -100.
So sum of the odd terms = 100/2*(1 + 99) [Sum of n terms of AP]
Again, sum of the even terms = 100/2*(-2 -100) [Sum of n terms of AP]
Total sum = 50*(100 -2 -100) = 50*(-2) = -100
Hence average = -100/200 = -1/2

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