Academic session 2026-27, Chapter 8 in the current curriculum.
Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter Sequence and Series. This page offers a step-by-step solution to the specific question from Exercise 2, Question 9: The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms.. With detailed answers and explanations for each chapter, students can strengthen their understanding and prepare confidently for exams. Ideal for CBSE and other board students, this resource will simplify your study experience.
Let a1, a2, and d1, d2 be the first terms and the common difference of the first and second arithmetic progression respectively.
According to the given condition,
\begin{align} \frac{Sum \;of \;n \;terms \;of \;first\; A.P.}{Sum\; of \;n\; terms \;of \;second \;A.P.} = \frac{5n+4}{9n+6} \end{align}
\begin{align} ⇒\frac{\frac{n}{2}\left[2a_1 + (n-1)d_1\right]}{\frac{n}{2}\left[2a_2 + (n-1)d_2\right]} = \frac{5n+4}{9n+6} \end{align}
\begin{align} ⇒\frac{2a_1 + (n-1)d_1}{2a_2 + (n-1)d_2} = \frac{5n+4}{9n+6} \;\;\;\;...(1)\end{align}
Substituting n = 35 in (1), we obtain
\begin{align} ⇒\frac{2a_1 + 34d_1}{2a_2 + 34d_2} = \frac{5(35)+4}{9(35)+6} \end{align}
\begin{align} ⇒\frac{a_1 + 17d_1}{a_2 + 17d_2} = \frac{179}{321} \;\;\;\;...(2)\end{align}
\begin{align} \frac{18^{th} \;term \;of\; first\; A.P.}{18^{th} \;term \;of\; second\; A.P.}=\frac{a_1 + 17d_1}{a_2 + 17d_2} \;\;\;\;...(3)\end{align}
From (2) and (3), we obtain
\begin{align} \frac{18^{th} \;term \;of\; first\; A.P.}{18^{th} \;term \;of\; second\; A.P.}=\frac{179}{321}\end{align}
Thus, the ratio of 18th term of both the A.P.s is 179: 321.
NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:
Stay updated with our latest educational content and study tips
It’s not about starting over if you took a break to care for children, take care of yourself, be healthy or for any other reason. This is a realistic strategy for the recovery of skills, selection of the right job, and overcoming the resume problem. One year, three years or 10 years of a career … Read more
Read MoreThere’s no need to score 95% or achieve a JEE/NEET rank. You don’t need to score 95% or rank in JEE/NEET to build a solid career. A candid and pragmatic guide to the routes that actually work for students who have an average mark and what to do when faced with the options. If … Read more
Read MoreAI tools, online platforms that are much cheaper than coaching centres and the changing idea of what “structure” even means have upended this argument more in the past two years than in the decade preceding it. Here’s what is really the case for 2026 – and what has actually stayed the same. If you look … Read more
Read MoreStarting to make a new career after 30 isn’t a start from scratch. Marketing, teaching, financial, retail, healthcare, sales and other professionals can pursue careers in technology by applying the existing knowledge and skills they have acquired to new technology skills. There are various ways to enter the technology industry, such as in IT support, … Read more
Read MoreCalculate percentage from obtained marks and total marks.
Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 2 , Question 9: The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio o....
Fresh educational articles and updates.
Most-read articles from SaralStudy.
Fast access to frequently used study resources.
Recently viewed articles based on SaralStudy activity.
Comments
We take 35 because. . If the ratio of the sum of n terms of ap is given, then to find the ratio of their nth terms, we replace n by (2n-1) in the ratio of the sums of n terms. 2*18-1 = 35
TO OBTAIN THE 18TH TERMS (n-1)/2=18-1 (n-1)/2=17 n-1=34 n=34+1 n=35
Why do we take n=35 in (1)?pls tell me
(n-1)/2=An-1
Why do we take n=35 in (1)?