5. Find the number of terms in each of the following A.P.(i) 7, 13, 19, …, 205

(i) Given, 7, 13, 19, …, 205 is the A.P Therefore First term, a = 7 Common difference, d = a2 − a1 = 13 − 7 = 6 Let there are n terms in this A.P. an = 205 As we know, for an A.P., an = a + (n − 1) d Therefore, 205 = 7 + (n − 1) 6 198 = (n − 1) 6 33 = (n − 1) n = 34 Therefore, this given series has 34 terms in it.