If the n^{th} term of the A.P. 9, 7, 5, ldots | vedclass

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(A) For the first $A.P.$: $a_1 = 9$,$d_1 = 7 - 9 = -2$. The $n^{th}$ term is $a_n = a_1 + (n - 1)d_1 = 9 + (n - 1)(-2) = 9 - 2n + 2 = 11 - 2n$.For the

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$7$

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(A) For the first $A.P.$: $a_1 = 9$,$d_1 = 7 - 9 = -2$. The $n^{th}$ term is $a_n = a_1 + (n - 1)d_1 = 9 + (n - 1)(-2) = 9 - 2n + 2 = 11 - 2n$.For the second $A.P.$: $a_2 = 15$,$d_2 = 12 - 15 = -3$. The $n^{th}$ term is $a_n = a_2 + (n - 1)d_2 = 15 + (n - 1)(-3) = 15 - 3n + 3 = 18 - 3n$.Since the $n^{th}$ terms are equal: $11 - 2n = 18 - 3n$.Rearranging the terms: $3n - 2n = 18 - 11$.Therefore,$n = 7$.

If the $n^{th}$ term of the $A.P.$ $9, 7, 5, \ldots$ and the $n^{th}$ term of the $A.P.$ $15, 12, 9, \ldots$ are equal,find the value of $n$.

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