For what value of n are the nth term of the following two A.P's the sa

1.	For what value of n are the nth term of the following two A.P's the same. Also find this term 63, 65, 67, ... and 3, 10, 17, ....
Answer» 1^st AP = 63, 65, 67, ... Here, a = 63, d = 65 – 63 = 2 and 2^nd AP = 3, 10, 17, ... Here, a = 3, d = 10 – 3 = 7 According to the question, 63 + (n – 1)2 = 3 + (n – 1)7 ⇒ 63 + 2n – 2 = 3 + 7n – 7 ⇒ 61 + 2n = 7n – 4 ⇒ 65 = 7n – 2n ⇒ 5n = 65 ⇒ n = 13 13^th term of the given AP’s are same. Now, we will find the 13^th term We have, a_n = a + (n – 1)d a₁₃ = 63 + (13 – 1)2 a₁₃ = 63 + 12 × 2 a₁₃ = 63 + 24 a₁₃ = 87

For what value of n are the nth term of the following two A.P's the same. Also find this term 63, 65, 67, ... and 3, 10, 17, ....

Answer»

1^st AP = 63, 65, 67, ...

Here, a = 63, d = 65 – 63 = 2

and 2^nd AP = 3, 10, 17, ...

Here, a = 3, d = 10 – 3 = 7

According to the question,

63 + (n – 1)2 = 3 + (n – 1)7

⇒ 63 + 2n – 2 = 3 + 7n – 7

⇒ 61 + 2n = 7n – 4

⇒ 65 = 7n – 2n

⇒ 5n = 65

⇒ n = 13

13^th term of the given AP’s are same.

Now, we will find the 13^th term

We have,

a_n = a + (n – 1)d

a₁₃ = 63 + (13 – 1)2

a₁₃ = 63 + 12 × 2

a₁₃ = 63 + 24

a₁₃ = 87