Q. 164.0( 2 Votes )

The sum of the 5<

Answer :

Given the sum of the 5th and 9th terms of an AP is 30.


We know that the nth term of an AP, an = a + (n – 1) d.


a5 = a + (5 – 1) d = a + 4d


a9 = a + (9 – 1) d = a + 8d


As given, a + 4d + a + 8d = 30


2a + 12d = 30 … (1)


Also given 25th term is three times its 8th term.


a25 = a + (25 – 1) d = a + 24d


a8 = a + (8 – 1) d = a + 7d


As given, a + 24d = 3 (a + 7d)


a + 24d = 3a + 21d


-2a + 3d = 0 … (2)


Solving the (1) and (2) equations,


15d = 30


d = 2


Substituting d = 2 in (2),


-2a + 6 = 0


6 = 2a


a = 3


Now, we got the first term, a = 3 and the common difference, d = 2,


The AP is as follows: 3, 5, 7, 9, …


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Glimpses of IndiaGlimpses of IndiaGlimpses of India39 mins
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