Q. 17 B5.0( 1 Vote )

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

23, 25, 27, 29, ... and – 17, – 10, – 3, 4, ...

Answer :

1st AP = 23, 25, 27, 29, ...


Here, a = 23, d = 25 – 23 = 2


and 2nd AP = – 17, – 10, – 3, 4, ...


Here, a = –17, d = –10 – (–17) = –10 + 17 = 7


According to the question,


23 + (n – 1)2 = –17 + (n – 1)7


23 + 2n – 2 = –17 + 7n – 7


21 + 2n = –24 + 7n


2n – 7n = –24 – 21


–5n = –45


n = 9


9th term of the given AP’s are same.


Now, we will find the 9th term


We have,


an = a + (n – 1)d


a9 = 23 + (9 – 1)2


a9 = 23 + 8 × 2


a9 = 23 + 16


a9 = 39


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