If the sum of the 3^{text{rd}} and the 8^{tex | vedclass

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(D) Let the first term and common difference of an $AP$ be $a$ and $d,$ respectively.According to the question,$a_{3} + a_{8} = 7$ and $a_{7} + a_{14}

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$-1$

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(D) Let the first term and common difference of an $AP$ be $a$ and $d,$ respectively.According to the question,$a_{3} + a_{8} = 7$ and $a_{7} + a_{14} = -3$Using the formula $a_{n} = a + (n - 1)d$:$(a + 2d) + (a + 7d) = 7 \Rightarrow 2a + 9d = 7$ ....$(i)$$(a + 6d) + (a + 13d) = -3 \Rightarrow 2a + 19d = -3$ ....$(ii)$Subtracting Eq. $(i)$ from Eq. $(ii)$:$(2a + 19d) - (2a + 9d) = -3 - 7$$10d = -10 \Rightarrow d = -1$Substituting $d = -1$ in Eq. $(i)$:$2a + 9(-1) = 7$$2a - 9 = 7 \Rightarrow 2a = 16 \Rightarrow a = 8$The $10^{	ext{th}}$ term is $a_{10} = a + 9d = 8 + 9(-1) = 8 - 9 = -1$.

If the sum of the $3^{\text{rd}}$ and the $8^{\text{th}}$ terms of an $AP$ is $7$ and the sum of the $7^{\text{th}}$ and the $14^{\text{th}}$ terms is $-3,$ find the $10^{\text{th}}$ term.

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