For what value of n,are the n^{th} terms of t | vedclass

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(A) For the first $AP: 63, 65, 67, \ldots$Here,first term $a = 63$ and common difference $d = 65 - 63 = 2$.The $n^{th}$ term is $a_n = a + (n - 1)d =

Vedclass · Accepted Answer

$13$

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(A) For the first $AP: 63, 65, 67, \ldots$Here,first term $a = 63$ and common difference $d = 65 - 63 = 2$.The $n^{th}$ term is $a_n = a + (n - 1)d = 63 + (n - 1)2 = 63 + 2n - 2 = 61 + 2n$.For the second $AP: 3, 10, 17, \ldots$Here,first term $a = 3$ and common difference $d = 10 - 3 = 7$.The $n^{th}$ term is $a_n = a + (n - 1)d = 3 + (n - 1)7 = 3 + 7n - 7 = 7n - 4$.Given that the $n^{th}$ terms are equal:$61 + 2n = 7n - 4$$61 + 4 = 7n - 2n$$65 = 5n$$n = 13$.Thus,the $13^{th}$ terms of both $APs$ are equal.

For what value of $n$,are the $n^{th}$ terms of two $APs: 63, 65, 67, \ldots$ and $3, 10, 17, \ldots$ equal?

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