For What Values Of N, Are The Nth Terms Of Two APs: 63,65,67,... And 3,10,17,...Equal?

To do:  Find for what values of N are the $n^th$ terms of two APs:   APs: 63,65,67,... And 3,10,17,...Equal

Solution:

To solve this we need to use the formula $n^th $term = $a + (n-1)d$

For first AP, common difference is : $65-63 = 2$

For second AP ,common difference is : $10-3 = 7$

Now Let the nth term be $A_n \ and \ B_n$ respectively.

According to question;

$A_n = B_n$

$=> 63+(n-1)2 = 3+(n-1)7$

$=>60 + 2n-2 = 7n-7$

$=>65 = 5n$

$=> n = 13$

Thus 13th term of both AP's will be same

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Updated on: 10-Oct-2022

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