Find the number of terms in each of the following APs :

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

(ii)

To find: Number of terms, n
(i) Given:  a = 7, d = 6, a_n = 205, n = ?

We know that nth term of an AP is given by,  a_n = a + (n – 1)d

205 = 7 + (n – 1)6

(n – 1)6 = 205 – 7 = 198

n – 1 = 33

n = 34

Thus, 205 is the 34th of term of this AP.

(ii) Given: a = 18, d = 15.5 – 18 = - 2.5, a_n = - 47

We know that nth term of an AP is given by,  a_n = a + (n – 1)d

Or, - 47 = 18 + (n – 1)(- 2.5)

Or, (n – 1)(- 2.5) = - 47 – 18 = - 65

Or, n – 1 = 26

Or, n = 27

Thus, - 47 is the 27th term of this AP.