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Class 10 > Learn Mathematics > If the 3rd and the 9th terms of an A.P are 4 and -8...
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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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Let the first term and the common difference are a and b. So, the third term: t3=a + 2b=4. and, the 9th term: t9=a + 8b=-8. So, t9 - t6=6b = -8 - 4=-12 --> b = - 2. So, from the expression of t3, we get: a = 4 - 2b = 4 + 4 = 8. Let us consider that the nth term is zero. So: tn...
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Let the first term and the common difference are a and b. So, the third term: t3=a + 2b=4. and, the 9th term: t9=a + 8b=-8. So, t9 - t6=6b = -8 - 4=-12 --> b=- 2. So, from the expression of t3, we get: a=4 - 2b=4 + 4=8. Let us consider that the nth term is zero. So: tn=a + (n-1)b = 0 --> 8 + (n-1)(-2) = 0 --> 8 -2n +2 = 0 --> 2n=10 --> n = 5. Answer: The 5th term of the series is zero. read less
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