Question

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

Answer 1

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.