The question is given from NCERT Book of class 10th Chapter no. 5 Ex. 5.2 Q. 9. In the following question you have to find which term will be zero if 3rd term is 4 & 9th term is -8. Give the solution.
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Which term of this A.P. is zero. If the 3rd and the 9th terms of an A.P. are 4 and − 8.
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Solution:
3rd term, a3 = 4
9th term, a9 = −8
We know ,
an = a+(n−1)d
Hence,
a3 = a+(3−1)d
4 = a+2d ……………………… (i)
a9 = a+(9−1)d
−8 = a+8d ……………………… (ii)
By subtracting (i) from (ii),
−12 = 6d
d = −2
From eq. (i),
4 = a + 2(−2)
4 = a − 4
a = 8
Let the nth term term of the A.P. be zero.
an = a + (n−1)d
0 = 8 + (n−1)(−2)
0 = 8 − 2n+2
2n = 10
n = 5
The 5th term of this A.P. is 0.