Which term of the A.P. 63, 65, 67, ldots and | vedclass

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(A) For the first $A.P.$: $a_1 = 63$,$d_1 = 65 - 63 = 2$. The $n^{th}$ term is $a_n = a_1 + (n - 1)d_1 = 63 + (n - 1)2 = 63 + 2n - 2 = 61 + 2n$.For th

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$13$

Vedclass · Answer

(A) For the first $A.P.$: $a_1 = 63$,$d_1 = 65 - 63 = 2$. The $n^{th}$ term is $a_n = a_1 + (n - 1)d_1 = 63 + (n - 1)2 = 63 + 2n - 2 = 61 + 2n$.For the second $A.P.$: $a_2 = 3$,$d_2 = 10 - 3 = 7$. The $n^{th}$ term is $a_n = a_2 + (n - 1)d_2 = 3 + (n - 1)7 = 3 + 7n - 7 = 7n - 4$.Equating the two $n^{th}$ terms: $61 + 2n = 7n - 4$.$61 + 4 = 7n - 2n$.$65 = 5n$.$n = 13$.Thus,the $13^{th}$ term of both sequences is equal.

Which term of the $A.P.$ $63, 65, 67, \ldots$ and $3, 10, 17, \ldots$ are equal (in $^{th}$)?

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