Find the number of terms in each of the following A.P.
(i) 7, 13, 19, …, 205
(ii) 18,
, 13,...., -47
(i) For this A.P.,
a = 7
d = a2 − a1 = 13 − 7 = 6
Let there are n terms in this A.P.
an = 205
We know that
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.
(ii) For this A.P.,
a = 18
Let there are n terms in this A.P.
an = 205
an = a + (n − 1) d
-47 = 18 + (n - 1) (-5/2)
-47 - 18 = (n - 1) (-5/2)
-65 = (n - 1)(-5/2)
(n - 1) = -130/-5
(n - 1) = 26
n = 27
Therefore, this given A.P. has 27 terms in it.
