Q17 of 176 Page 8

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

24, 20, 16, 12, ... and – 11, – 8, – 5, – 2, ...

1st AP = 24, 20, 16, 12, ...


Here, a = 24, d = 20 – 24 = –4


and 2nd AP = – 11, – 8, – 5, – 2, ...


Here, a = –11, d = –8 – (–11) = –8 + 11 = 3


According to the question,


24 + (n – 1)(–4) = –11 + (n – 1)3


⇒ 24 – 4n + 4 = –11 + 3n – 3


⇒ 28 – 4n = –14 + 3n


⇒ 28 + 14 = 3n + 4n


⇒ 7n = 42


⇒ n = 6


6th term of the given AP’s are same.


Now, we will find the 6th term


We have,


an = a + (n – 1)d


a6 = 24 + (6 – 1)(–4)


a6 = 24 + 5 × –4


a6 = 24 – 20


a6 = 4


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