Answer :

Given:

T10 = –4


T22 = –16


We know that,


nth term = Tn = a + (n – 1)d


where,


a = first term


d = common difference



T10 = a + (10 – 1)d = -4


a + 9d = -4 (1)


And,


T22 = a + (22 – 1)d = -16


a + 21d = -16 …(2)


Subtract (1) from (2),


(a + 21d) – (a + 9d) = -16 – (-4)


a + 21d a 9d = -16 + 4


12d = -12


d = -1


Put value of d in (1),


a + 9d = -4


a + 9(-1) = -4


a 9 = -4


a = -4 + 9


a = 5


Now,


T38 = 5 + (38 – 1)(-1)


T38 = 5 + 37(-1)


T38 = 5 – 37


T38 = – 32


Hence, the 38th term is – 32


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses