The 7^{th} and 12^{th} terms of an A.P. are 4 | vedclass

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(A) Let the first term of the $A.P.$ be $a$ and the common difference be $d$.The $n^{th}$ term of an $A.P.$ is given by $T_n = a + (n - 1)d$.For the $

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$5n + 11$

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(A) Let the first term of the $A.P.$ be $a$ and the common difference be $d$.The $n^{th}$ term of an $A.P.$ is given by $T_n = a + (n - 1)d$.For the $7^{th}$ term: $T_7 = a + 6d = 46$  --- $(1)$For the $12^{th}$ term: $T_{12} = a + 11d = 71$  --- $(2)$Subtracting equation $(1)$ from equation $(2)$:$(a + 11d) - (a + 6d) = 71 - 46$$5d = 25$$d = 5$Substituting $d = 5$ in equation $(1)$:$a + 6(5) = 46$$a + 30 = 46$$a = 16$The $n^{th}$ term is $T_n = a + (n - 1)d = 16 + (n - 1)5 = 16 + 5n - 5 = 5n + 11$.

The $7^{th}$ and $12^{th}$ terms of an $A.P.$ are $46$ and $71$ respectively. Find the $n^{th}$ term of the $A.P.$

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