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, ...
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
AI is thinking…
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.