Q. 17 D4.0( 2 Votes )

For what value of n are the nth term of the following two A.P's the same. Also find this term

63, 65, 67, ... and 3, 10, 17, ...

Answer :

1st AP = 63, 65, 67, ...


Here, a = 63, d = 65 – 63 = 2


and 2nd AP = 3, 10, 17, ...


Here, a = 3, d = 10 – 3 = 7


According to the question,


63 + (n – 1)2 = 3 + (n – 1)7


63 + 2n – 2 = 3 + 7n – 7


61 + 2n = 7n – 4


65 = 7n – 2n


5n = 65


n = 13


13th term of the given AP’s are same.


Now, we will find the 13th term


We have,


an = a + (n – 1)d


a13 = 63 + (13 – 1)2


a13 = 63 + 12 × 2


a13 = 63 + 24


a13 = 87


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