(i) 7, 13, 19, . . . , 205

(ii) 18, 15 ½ , 13, . . . , – 47

**Solution:**

**(i) 7, 13, 19, . . . , 205**

Here,

First term, a = 7

Common difference, d = a_{2} − a_{1} = 13 − 7 = 6

Let n be the number of terms in the given AP.

a_{n} = 205

We know that,

a_{n} = a + (n − 1) d

205 = 7 + (n − 1) 6

198 = (n − 1) 6

33 = (n − 1)

n = 34

Therefore, the given AP has 34 terms in it.

**(ii) 18, 15 ½ , 13, . . . , –47**

Here,

First term, a = a_{1} = 18

Common difference, d = a_{2} − a_{1} = 15 ½ – 18 = (31/2) – 18 = -5/2

Let n be the number of terms in the given AP.

a_{n} = -47

We know that,

a_{n} = a + (n − 1) d

-47 = 18 + (n – 1)(-5/2)

-47 – 18 = (n – 1)(-5/2)

-65 × (-2/5) = (n – 1)

26 = n – 1

n = 27

Therefore, the given AP has 27 terms in it.