If the 3^{rd} and the 9^{th} terms of an AP a | vedclass

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(C) Given that,the $3^{rd}$ term $a_3 = 4$ and the $9^{th}$ term $a_9 = -8$.We know the formula for the $n^{th}$ term of an $AP$ is $a_n = a + (n - 1)

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$5$

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(C) Given that,the $3^{rd}$ term $a_3 = 4$ and the $9^{th}$ term $a_9 = -8$.We know the formula for the $n^{th}$ term of an $AP$ is $a_n = a + (n - 1)d$.For the $3^{rd}$ term: $a + 2d = 4$ $...(i)$For the $9^{th}$ term: $a + 8d = -8$ $...(ii)$Subtracting equation $(i)$ from $(ii)$:$(a + 8d) - (a + 2d) = -8 - 4$$6d = -12$$d = -2$Substituting $d = -2$ in equation $(i)$:$a + 2(-2) = 4$$a - 4 = 4$$a = 8$Now,let the $n^{th}$ term be zero,so $a_n = 0$:$0 = a + (n - 1)d$$0 = 8 + (n - 1)(-2)$$0 = 8 - 2n + 2$$2n = 10$$n = 5$Thus,the $5^{th}$ term of this $AP$ is zero.

If the $3^{rd}$ and the $9^{th}$ terms of an $AP$ are $4$ and $-8$ respectively,which term of this $AP$ is zero?

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