find the 31st term of an ap if the 3rd term is 4 and 9th term is -8 which term of A.P is zero
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Answer:
31st term = -52
5th term = 0
Although without any proof we can get that 31st term = -52 and 5th term = 0, but we need to find the results by generalized process as follows.
Step-by-step explanation:
3rd term = 4
9th term = -8
number of terms between the 3rd term and 9th term = n = (9-3)-1 = 5
common difference = d = (9th term - 3rd term)/(n+1) = (-8-4)/6 = -12/6 = -2
1st term = a = (3rd term - 2d) = 4 - 2×(-2) = 4 + 4 = 8
31st term = a + (31-1)×d = 8 + 30×(-2) = 8 - 60 = -52
let nth term = 0
=> a + (n-1)×d = 0
=> 8 + (n-1)×(-2) = 0
=> 8 -2n + 2 = 0
=> 2n = 10
=> n = 10/2 = 5
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