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Arithmetic Progressions
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31/05/2021 11:32 am
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If the 3rd and the 9th terms of an A.P. are 4 and -8 respectively. Which term of this A.P. is zero.
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31/05/2021 11:34 am
Given that,
3rd term, a3 = 4
and 9th term, a9 = -8
We know that,
an = a+(n−1)d
Therefore,
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 will get here,
−12 = 6d
d = −2
From equation (i), we can write,
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.