Question

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 1

1^st AP = 23, 25, 27, 29, ...

Here, a = 23, d = 25 – 23 = 2

and 2^nd 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

9^th term of the given AP’s are same.

Now, we will find the 9^th term

We have,

a_n = a + (n – 1)d

a₉ = 23 + (9 – 1)2

a₉ = 23 + 8 × 2

a₉ = 23 + 16

a₉ = 39