Q. 17 C5.0( 2 Votes )

# For what value of n are the nth term of the following two A.P's the same. Also find this term24, 20, 16, 12, ... and – 11, – 8, – 5, – 2, ...

Answer :

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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