Question

if the nth term of the AP 9,7,5,... and the nth term of the AP 15,12,9,... are equal, find the value of n

Answer 1

HOPE IT HELPS YOU..............

Answer 2

Answer:

Let us consider AP 1 = 9, 7, 5, 3, ...

Here, a = 9, d = ( -2 ), n = n

Let us consider AP 2 = 15, 12, 9, 6, ...

Here, a = 15, d = ( -3 ), n = n

$a_{n_1} = a_{n_2}\\\\\implies a_{n_1} = 9 + ( n - 1 ) ( -2 )\\\\\implies a_{n_2} = 15 + ( n - 1 ) ( - 3 )$

Equating them we get,

⇒ 9 + ( n - 1 ) ( - 2 ) = 15 + ( n - 1 ) ( - 3 )

⇒ 9 + ( -2n + 2 ) = 15 + ( -3n + 3 )

⇒ 9 + 2 - 2n = 15 + 3 - 3n

⇒ 11 - 2n = 18 - 3n

Transposing all the n terms to one side we get,

⇒ 3n - 2n = 18 - 11

⇒ n = 7

Hence the value of n is 7.