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Questions
If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?
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
Given that,
a3 = 4
a9 = −8
We know that,
an = a + (n − 1) d
a3 = a + (3 − 1) d
4 = a + 2d ...(I)
a9 = a + (9 − 1) d
−8 = a + 8d ...(II)
On subtracting equation (I) from (II), we obtain
−12 = 6d
d = −2
From equation (I), we obtain
4 = a + 2 (−2)
4 = a − 4
a = 8
Let nth term of this A.P. be zero.
an = a + (n − 1) d
0 = 8 + (n − 1) (−2)
0 = 8 − 2n + 2
2n = 10
n = 5
Hence, 5th term of this A.P. is 0.
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