The sum of the 5^{text{th}} and the 7^{text{t | vedclass

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(D) Let the first term be $a$ and the common difference be $d$ of the $AP$.According to the question:$a_5 + a_7 = 52$ and $a_{10} = 46$.Using the form

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$1, 6, 11, 16, \ldots$

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(D) Let the first term be $a$ and the common difference be $d$ of the $AP$.According to the question:$a_5 + a_7 = 52$ and $a_{10} = 46$.Using the formula $a_n = a + (n-1)d$:$(a + 4d) + (a + 6d) = 52$$2a + 10d = 52$$a + 5d = 26$ ..... $(i)$Also,$a_{10} = 46$:$a + 9d = 46$ ..... $(ii)$Subtracting equation $(i)$ from equation $(ii)$:$(a + 9d) - (a + 5d) = 46 - 26$$4d = 20$$d = 5$Substituting $d = 5$ in equation $(i)$:$a + 5(5) = 26$$a + 25 = 26$$a = 1$The $AP$ is given by $a, a+d, a+2d, a+3d, \ldots$Substituting the values: $1, 1+5, 1+10, 1+15, \ldots$Thus,the $AP$ is $1, 6, 11, 16, \ldots$

The sum of the $5^{\text{th}}$ and the $7^{\text{th}}$ terms of an $AP$ is $52$ and the $10^{\text{th}}$ term is $46$. Find the $AP$.

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