# The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.

Let a1, a2, and d1, d2 be the first terms and the common difference of the first and second arithmetic progression respectively.

Given: We know that Sum of n terms of an A.P is given by, where, n = number of terms, a = first term and d = common difference of A.P.

So now we have,  Now as we need to find the ratio of first 17 terms, we want the numerator and denominator of the form (a + 17 d)
2 a1 + (n - 1) d1 = a + 17 d
So we need to multiply R.H.S by 2 and we get,
2 a1 + (n - 1) d = 2 a + 34 d
Equating the terms we get,
n - 1 = 34, n = 35.

Putting n = 35 in the above equation    Thus, the ratio of 18th term of both the A.P.s is 179: 321

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Sequence & Series (Lecture 1)56 mins  Check Your progress Part 2| Interactive Quiz: Sequence & Series47 mins  Sequence & Series (Lecture 5)42 mins  Sequence & Series (Lecture 7)37 mins  Interactive quiz on inequalities involving AM and GM45 mins  Use of sigma in finding sum42 mins  Sequence & Series (Lecture 6)42 mins  Sequence & Series (Lecture 8)35 mins  Check Your progress Part 3| Interactive Quiz: Sequence & Series46 mins  Trigonometric Series45 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 view all courses 