The question is given from NCERT Book of class 10th Ch. no. 5 Ex. 5.2 Q. 8. In the following question you have to find which term in this series will be zero if 3rd term is 4 & 9th term is -8.
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If the 3rd and 9th terms of an A.P. are 4 and − 8 respectively. Which term in this A.P. is zero.
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Solution:
3rd term, a3 = 12
50th term, a50 = 106
We know,
an = a+(n−1)d
a3 = a+(3−1)d
12 = a + 2d ……………………………. (i)
Like this,
a50 = a + (50−1)d
106 = a + 49d …………………………. (ii)
By subtracting (i) from (ii),
94 = 47d
d = 2
From equation (i),
12 = a + 2(2)
a = 12 − 4 = 8
a29 = a + (29−1) d
a29 = 8 + (28)2
a29 = 8 + 56 = 64
The 29th term of the give A.P is 64.