(Q19).Find the number of terms in each of the following APs :

(ii) 18, 15
1
2
 , 13, …, -47

Given: A.P: 18, 15
1
2
 , 13, …….

Here a1 = a = ;

d = a2 – a1 =
1
– = -
1
= -

Let ‘-’ be the nth term of the given A.P.

an = a + (n – 1) d

⇒ - = + (n-1)×(
-
 )
⇒ - =
×+(n-1)(-)

⇒ - = – n +

⇒ n = +

n =
=

∴ terms are there.