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 term23, 25, 27, 29, ... and – 17, – 10, – 3, 4, ...

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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