Careers360 Logo
Browse by Stream
Search Colleges, Exams, Schools & more
JEE Main Preparation Tips for Maths
  1. Home
  2. JEE Main
  3. Study Material
  4. Sum of n Terms of an AP - Practice Questions & MCQ

Sum of n Terms of an AP - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Sum of n terms of an AP is considered one the most difficult concept.

  • 46 Questions around this concept.

Solve by difficulty

QuestionEASY

Let \; a_{1},a_{2},a_{3},.... be terms of an A.P. If \frac{a_{1}+a_{2}+......+a_{p}}{a_{1}+a_{2}+......+a_{q}}=\frac{p^{2}}{q^{2}},p\neq q,  then \; \frac{a_{6}}{a_{21}}\; equals:

View Solution

Concepts Covered - 1

Sum of n terms of an AP

The sum, Sn  of n terms of an AP with the first term ‘a’ and common difference ‘d’ is given by  

\begin{array}{l}{S_{n}=\frac{n}{2}[2 a+(n-1) d]} \\ {\text { OR }} \\ {S_{n}=\frac{n}{2}[a+l]} \\ {a \rightarrow \text { first term }} \\ {d \rightarrow \text { common difference }} \\ {n \rightarrow \text { number of terms }}\end{array}

 

\\\begin{array}{l}{S_{n}=a+(a+d)+(a+2 d)+\ldots . .+(a+(n-2) d)+(a+(n-1) d) \ldots \ldots .(i)} \\ {\text {Rewrite}} \\ {S_{n}=(a+(n-1) d)+(a+(n-2) d)+\ldots \ldots \ldots+(a-2 d)+(a-d)+a \ldots \ldots(i i)} \\ {(i)+(i i)}\end{array}\\\begin{array}{l}{2 S_{n}=(2 a+(n-1) d)+(2 a+(n-1) d+\ldots \ldots \ldots \ldots . . . . \text { upto } n \text { term }} \\ {S_{n}=\frac{n}{2}[(2 a+(n-1) d)]}\end{array}\\\begin{array}{l}{\text {Also, } a+(n-1) d=l=\text {last term}} \\ {\text {we can also write }} \\ {S_{n}=\frac{n}{2}[a+a+(n-1) d]=\frac{n}{2}[a+l]}\end{array}

Study it with Videos

Sum of n terms of an AP

Study other Related Concepts

Sum of n Terms of an AP Current Topic

Sequence And Series
Arithmetic Progression
Sum of n Terms of an AP
Arithmetic Mean in AP
Geometric Progression
Geometric Mean In GP
Sum To n Terms Of a GP
Harmonic Progression
Harmonic Mean in HP
Relation between A.M., G.M. and H.M.

"Stay in the loop. Receive exam news, study resources, and expert advice!"

Books

Reference Books

Sum of n terms of an AP

Mathematics for Joint Entrance Examination JEE (Advanced) : Algebra

Page No. : 5.7

Line : 1

Clear your Basics with NCERT

E-books & Sample Papers

JEE Main 2025 Chapter Wise Weightage

1350+ Downloads

Get Answer to all your questions

JEE Main Articles

JEE Main Syllabus with Weightage 2025 PDF Free Download
Oct 04, 2024
JEE Main Cutoff 2024 (Out) - Qualifying Marks for NITs, IIITs, GFTIs
Oct 03, 2024
Documents Required for JEE Main 2025 Registration
Oct 03, 2024
JEE Main Age Limit 2025 - Check Age Limit
Oct 03, 2024
JEE Main 2025 - Exam Date, Eligibility, Registration, Preparation Tips, Previous Year Papers
Oct 03, 2024
JEE Main Exam Pattern 2025 - Total Marks in JEE Mains, Paper Pattern, Marking Scheme
Oct 03, 2024
JEE Main Exam Date 2025 - NTA JEE Mains Session 1 & 2 Exam Schedule
Oct 03, 2024
JEE Main Marks vs Rank 2024 - Calculate JEE Mains Rank using Marks
Oct 03, 2024

B.Tech/B.Arch Admissions OPEN

Amity University, Noida B.Tech Admissions 2024
Amity University, Noida B.Tech Admissions 2024
Apply

Asia's Only University with the Highest US & UK Accreditation

JSS University Noida Admissions 2024
JSS University Noida Admissions 2024
Apply

170+ Recruiters Including Samsung, Zomato, LG, Adobe and many more | Highest CTC 47 LPA

Atlas SkillTech University | B.Tech Admissions
Atlas SkillTech University | B.Tech Admissions
Apply

Hands on Mentoring and Code Coaching | Cutting Edge Curriculum with Real World Application

Plastindia International University B.Tech Admissions 2024
Plastindia International University B.Tech Admissions 2024
Apply

International Learning Opportunities | UGC Approved | State-of-the-Art Laboratories

Joy University B.Tech 2024
Joy University B.Tech 2024
Apply

Outstanding faculty of Eminence from IIT, BITS, IIM, IIIT NIT, NID and faculty from foreign universities | Merit & sports based scholarship

ICFAI University Hyderabad B.Tech Admissions 2024
ICFAI University Hyderabad B.Tech Admissions 2024
Apply

Merit Scholarships | NAAC A+ Accredited | Top Recruiters : E&Y, CYENT, Nvidia, CISCO, Genpact, Amazon & many more

View All Application Forms
News and Notifications
Over 656 UPSC, JEE, NEET, other coaching aspirants refunded more than Rs 1 crore: Govt
September 22, 2024 - 04:31 PM IST
NTA Exam Calendar 2025: JEE Main, NEET, CUET, UGC NET dates soon; websites to check
September 19, 2024 - 11:41 AM IST
JEE Main 2025 exam date soon; syllabus, previous years' question papers, books for preparation
September 13, 2024 - 04:35 PM IST
JEE Main 2025 exam date this month; updates on reduced syllabus, registration, number of attempts
September 03, 2024 - 07:24 PM IST
AP BArch Admission 2024: Registration begins today at apsche.ap.gov.in; eligibility criteria
August 12, 2024 - 11:27 AM IST
JoSAA 2024 round 4 seat allotment results out at josaa.nic.in; report online by July 15
July 10, 2024 - 07:26 PM IST
CSAB NEUT 2024 registration begins at csab.nic.in; apply by June 28
June 20, 2024 - 12:07 PM IST

Download Careers360 App's

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

  • student
    300M+

    Students

  • colleges
    36,000+

    Colleges

  • exams
    550+

    Exams

  • ebook
    1500+

    E-Books

  • certification
    16000+

    Certifications

student
Mobile Screen

We Appeared in

Joint Entrance Examination (Main)      
JEE Main 2025 Sample Papers
Back to top