Sum
If the 3rd and the 9th terms of an arithmetic progression are 4 and -8 respectively, Which term of it is zero?
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Solution
For an A.P
`t_3 = 4`
=> a +2d = 4 .....(i)
`t_9 = -8`
=> a + 8d = -8 ....(ii)
Substractinjg (i) from (ii) we get
6d = -12
=> d = -2
Substituting d = -2 in (i) we get
a + 2(-2) = 4
=> a - 4 = 4
=> a = 8
=> general term = `t_n = 8 + (n - 1)(-2)`
Let pth term of this A.P be 0
`=> 8 + (p - 1) xx (-2) = 0`
`=> 8 - 2p + 2 = 0`
=> 10 - 2p = 0
=> 2p = 10
=> p = 5
Thus 5th term of this A.P is 0.
Concept: Arithmetic Progression - Finding Their General Term
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