(i)-1,-5/6,-2/3,……………10/3
Solution:
First term = -1
a = -1
Common difference = t2 – t1
= (-5/6) – (-1)
= (-5/6) + 1
= (-5 + 6)/6
= 1/6
tn = 10/3
tn = a + (n - 1) d
10/3 = -1 + (n - 1) (1/6)
(10/3) + 1 = (n - 1) (1/6)
13/3 = (n - 1) (1/6)
(13/3)(6/1) = (n - 1)
26 = n -1
26 + 1= n
n = 27
Therefore 27 terms are in the given A.P
(ii)7,13,19,……………205
Solution:
First term = 7
a = 7
Common difference = t2 – t1
= 13 – 7
= 6
tn = 205
tn = a + (n - 1) d
205 = 7 + (n - 1) (6)
205 - 7 = (n - 1) (6)
198 = (n - 1) (6)
198/6 = (n - 1)
33 = n -1
33 + 1= n
n = 34
Therefore 34 terms are in the given A.P