For what value of n’. are the nth terms of two AP: 63, 65, 67, …�

1.	For what value of n’. are the nth terms of two AP: 63, 65, 67, ……. and 3, 10, 17, ……….. equal?
Answer» 63, 65, 67,………. a = 63. d = 65 – 63 = 2. a_n =? nth term of this is a_n = a + (n – 1)d = 63 + (n – 1) 2 = 63 + 2n – 2 an= 2n + 61 …………….. (i) 3, 10, 17, …………. a = 3, d = 10 – 3 = 7, a_n =? a_n = a + (n – 1)d = 3 + (n – 1)7 = 3 + 7n – 7 a_n = 7n — 4 ………….(ii) Here. n^th terms of second AP are equal. ∴ equation (i) = equation (ii) 2n + 61 = 7n – 4 2n – 7n = -4 – 61 5n = 65 5n =65 ∴ n = \(\frac{65}{5}\) ∴ n = 13 ∴13^th terms of the two given AP are equal.

For what value of n’. are the nth terms of two AP: 63, 65, 67, ……. and 3, 10, 17, ……….. equal?

Answer»

63, 65, 67,……….

a = 63. d = 65 – 63 = 2. a_n =?

nth term of this is

a_n = a + (n – 1)d

= 63 + (n – 1) 2

= 63 + 2n – 2

an= 2n + 61 …………….. (i)

3, 10, 17, ………….

a = 3, d = 10 – 3 = 7, a_n =?

a_n = a + (n – 1)d

= 3 + (n – 1)7

= 3 + 7n – 7

a_n = 7n — 4 ………….(ii)

Here. n^th terms of second AP are equal.

∴ equation (i) = equation (ii)

2n + 61 = 7n – 4

2n – 7n = -4 – 61 5n = 65

5n =65

∴ n = \(\frac{65}{5}\)

∴ n = 13

∴13^th terms of the two given AP are equal.