Ask & Answer: India's Largest Education Community

77. Let a and d be the first term and common difference of an A.P.

Then, 

$n_{}=\frac{n}{2}[2a+(n-1)d]=S_1$

$S_{2n}=\frac{2n}{2}[2a+(2n-1)d]=S_2$

$S_{3n}=\frac{3n}{2}[2a+(3n-1)d]=S_3$

Now, R.H.S $=3\left(S_2-S_1\right)$

$=3\left\{\frac{2n}{2}[2a+(2n-1)d]-\frac{x}{2}[2a+(n-1)d]\right\}$

$=\frac{3n}{2}\{2[2a+(2n-1)d-[2a+(x-1)d]\}$

$=\frac{3n}{2}\{4a+(4x-2)d-2a-(x-1)d\}$

$=\frac{3n}{2}\{2a+\left[4x-2\left(n-1\right)d\right]\}$

$=\frac{3n}{2}\{2a+[4n-2-n+1]d\}$

$=\frac{3n}{2}\{2a+[3n-1]d\}=S_3$

$\therefore S_3=3\left(S_2-s_1\right)$

Yes, K J Somaiya School of Engineering does follow a semester pattern for BTech course, which is divided into 8 semesters for four years on a Choice Based Credit System(CBCS). This systemic learning helps candidates to gain a wide range of subjects during this duration. 

R V Institute of Technology and Management  has been providing successful placements over the years for BTech students. Check out the table below to know the key highlights of the R V Institute of Technology and Management placement for BTech in 2023-2024:

R V Institute of Technology and Management  provides good placements to its graduating BTech students. Check out the table below to know the placement highlights of the R V Institute of Technology and Management for BTech in 2023-2024:

Somaiya School of Design, supported by Riidl offers a comprehensive BDes course for a duration of four years. For admission to this course, the institute accepts multiple entrance exams for admission to BDes courses. The below list showcases all the accepted entrance exams:

• SVUET
• UCEED
• NID DAT
• NIFT
• PERA-CET
• NATA
• JEE Main Paper 2
• MAH- Design CET

Those who have a valid score in any one of the aforementioned exams and fulfil the eligibility criteria can apply for the course on the institute's official website.

The K J Somaiya School of Engineering (KJSSE) BTech course is organized into eight semesters, including core engineering streams, practical training, and professional growth. During the first year of study, courses such as Applied Mathematics, Engineering Physics, Chemistry, and Programming are covered, along with workshops and communication skills.

During ISAB MBA placements 2025 over 150 offers have been made by 50 companies. The table below presents the same:

The highest package offered during  ISAB MBA placements 2025 was INR 8.5 LPA. Check out the data tabulated below to know more:

The MBA placement record at ISAB has been very impressive. Check out the table below to know more:

 ISAB has not released its placement rate yet. However they provide 100% placement assistance to all its students. Check out the placement highlights for 2025 given below:

In 2025 36 new recruiters took part in the placement season. In all 50 recruiting companies were a part of the placement season at ISAB. Refer to the table below for more:

The highest offered during ISAB placements was INR 8.5 LPA. The company that offered the package is not known yet. Once the information is available, it will be updated here. 

To crack ISAB placement interview students can follow the steps given below:

·       Review your resume

·       Practice common interview questions

·       Showcase your strengths

·       Be confident and articulate

Various companies visit ISAB for placements some of them are given below:

For preparation of an exam like CMAT will always be helpful as you will be provided with relevant study material and guidance from industry experts. It will help you in disciplined and focused study as coaching centres have time bound classes, lectures, practice sessions, mock tests, etc. So, if you feel that you will not be able to stay dedicated and motivated enough in self-study to crack CMAT will high scores, join a CMAT coaching institute.

CMAT is a highly competitive exam having five subjects – Quantitative Aptitude, Logical Reasoning, English Comprehension, General Awareness and Innovation & Entrepreneurship. These subjects have a lot of topic and sub-topics that one has to cover. Practicing only CMAT sample papers and mock tests will not be enough as to be able to solve all types of questions, one needs to have understood the topic or the concept. Thus, study the topics included in CMAT syllabus first and then practice CMAT sample papers and mock tests.

The average package for ISAB stood at  INR 5 LPA during 2025 placement drive. The table below states the same:

CMAT has five subjects – Quantitative Aptitude, Logical Reasoning, English Comprehension, General Awareness and Innovation & Entrepreneurship and to cover all of them, one will need good enough time. Overall, 3 months are needed to cover syllabus of CMAT and about 2 to 3 months for practice and revision. So, overall 6 months are good for CMAT preparation. 

ISAB has an impressive placement record. The placement statistics for 2025 are given in the table below: