For what value of $n$ , are the $n$ th terms of two APs : $63, 65, 67, . . .$ and $3, 10, 17, . . .$ equal

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Solution

$63, 65, 67$ $3, 10, 17$
$a = 63, d = z$ $a^{'} = 3, d^{'} = 7$
$63 + (n - 1) 2 = 3 + (n - 1) 7$
$63 + 2 n - 2 = 3 + 7 n - 7$
$65 = 5 n$
$n = 13$

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