Question

If the n^th term of the A.P. 58, 60, 62, .... is equal to the n^th term of the A.P. –2, 5, 12, …., find the value of n.

Answer 1

In the first A.P. 58, 60, 62, ....

a = 58 and d = 2

t_n = a + (n – 1)d

⇒ t_n = 58 + (n – 1)2  ...(i)

In the first A.P. –2, 5, 12, ....

a = –2 and d = 7

t_n = a + (n – 1)d

`\implies` t_n= –2 + (n – 1)7  ...(ii)

Given that the n^th term of first A.P is equal to the n^th term of the second A.P.

`\implies` 58 + (n – 1)2 = –2 + (n – 1)7 …[From (i) and (ii)]

`\implies` 58 + 2n – 2 = –2 + 7n – 7

`\implies` 65 = 5n

`\implies` n = 13