Find the number of terms in each of the following APs :
(i) 7, 13, 19, . . . , 205
(ii)
(i) Here, a = 7, d = 6, an = 205, n = ?
We know that an = 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) Here, a = 18, d = 15.5 – 18 = - 2.5
We know that an = 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.