Mathematics
If the 3rd and the 9th terms of an A.P. are 4 and -8 respectively, then which term of the A.P. is zero ?
Answer
We know that
an = a + (n - 1)d
Given,
a3 = 4 and a9 = -8
∴ a + 2d = 4 and a + 8d = -8
Subtracting the two Equations,
⇒ a + 8d - (a + 2d) = -8 - 4
⇒ a - a + 8d - 2d = -12
⇒ 6d = -12
⇒ d = -2.
Putting value of d in a + 2d = 4
⇒ a + 2 × (-2) = 4
⇒ a - 4 = 4
⇒ a = 4 + 4
⇒ a = 8.
Let nth term of the A.P. be zero so, an = 0.
⇒ a + (n - 1)d = 0
⇒ 8 + (n - 1) × (-2) = 0
⇒ 8 - 2n + 2 = 0
⇒ 10 - 2n = 0
⇒ 2n = 10
⇒ n = 5.
Hence, the 5th term of the A.P. is zero.
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