In an AP of 200 terms sum of all even numbered terms is 2020 and sum of all odd numbered terms is 2019. Find common difference
Answers
Given : n an AP of 200 terms sum of all even numbered terms is 2020 and sum of all odd numbered terms is 2019
To find : common difference
Solution:
Let say AP is
a , a+d , a + 2d .............
Sum = (n/2)(2a + (n - 1)d)
odd numbered terms
a , a + 2d , a + 4d....
Sum of odd numbered terms
cd = 2d n = 100
(100/2)(2a + 99*2d) = 2019
=> 200 ( a + 99d) = 4038
even numbered terms
a + d , a + 3d , ............
cd = 2d n = 100 first term = a + d
Sum = (100/2)(2(a + d) + 99*2d) = 2020
=> 200(a + 100d) = 4040
=> 200(a + 100d) - 200(a + 99d) = 4040 - 4038
=> 200d = 2
=> d = 2/200
=> d = 1/100
Common difference = 1/100
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