UrbanPro
Login Ask & Answer Success Stories Paid Courses Free Classes Tuition & Classes Fees Write a Review All Categories Help Center
Post your Learning Need Signup as a Tutor
✕

Popular Cities

Bangalore

Hyderabad

Delhi

Mumbai

Chennai

Pune

Kolkata

Gurgaon

Ahmedabad

Jaipur

Noida

✕

Take Class 12 Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Book a Free Demo

Class 12 Tuition > The sum of first four terms of an A.P. is 56 . The...
✕

Search in

The sum of first four terms of an A.P. is 56 . The sum of last four terms is 112. If its first term is 11 then find the number of terms ?

Asked by Last Modified  

18 Answers

Follow 0
Answer

Please enter your answer

Tutor

Let the first term be 'a' Given:- a=11. Also, it is given that sum of its 1st four terms is 56, which means a + a + d + a + 2d + a + 3d=56 => 4a+6d = 56=> 44+6d = 56 Therefore, d=2 Again given that sum of last four terms is 112. a + (n-1) d + a + (n-2)d +...
read more
Let the first term be 'a' Given:- a=11. Also, it is given that sum of its 1st four terms is 56, which means a + a + d + a + 2d + a + 3d=56 => 4a+6d = 56=> 44+6d = 56 Therefore, d=2 Again given that sum of last four terms is 112. a + (n-1) d + a + (n-2)d + a + (n-3)d + a + (n-4)d = 112 putting a=11 and d=2 => 44+8n-20 = 112 So, solving this we get n=11. There are 11 terms in this A.P The series is 11,13,15,17,19,21,23,25,27,29,31. 11+13+15+17=56 31+29+27+25=112 read less
Comments
Dislike Bookmark

Tutor

The proof to the Rational Numbers question posted, is as follows:- A number 'n' can be partitioned without repetition in 'n-1' ways. So total number of partitions till 'n-1' let us call this j = 1/2 * (n-2) (n-1)...since there are n-2 partitions for 'n-1' Let this 'n'= p+q As the 1st term of 'n'...
read more
The proof to the Rational Numbers question posted, is as follows:- A number 'n' can be partitioned without repetition in 'n-1' ways. So total number of partitions till 'n-1' let us call this j = 1/2 * (n-2) (n-1)...since there are n-2 partitions for 'n-1' Let this 'n'= p+q As the 1st term of 'n' stars with q=1 p/q will be represented by (j+q)th term. read less
Comments
Dislike Bookmark

Tutor

The proof to the Rational Numbers question posted, is as follows:- A number 'n' can be partitioned without repetition in 'n-1' ways. So total number of partitions till 'n-1' let us call this j = 1/2 * (n-2) (n-1)...since there are n-2 partitions for 'n-1' Let this 'n'= p+q As the 1st term of 'n'...
read more
The proof to the Rational Numbers question posted, is as follows:- A number 'n' can be partitioned without repetition in 'n-1' ways. So total number of partitions till 'n-1' let us call this j = 1/2 * (n-2) (n-1)...since there are n-2 partitions for 'n-1' Let this 'n'= p+q As the 1st term of 'n' starts with q=1 p/q will be represented by (j+q)th term. read less
Comments
Dislike Bookmark

Trainer

Let the AP be a + (a +d)+ (a+2d)+ (a +3d) +....... .................... + a +(n-1)d + a +(n -2)d + a +(n-3)d +a +(n-4)d a + (a +d)+ (a+2d)+ (a +3d) = 56 4d + 6d = 56 since a = 11, d = 2 sum of the last 4 terms = 112 (n-1)d + a +(n -2)d + a +(n-3)d +a +(n-4)d =112 4a + (4n-10)d = 112 plug...
read more
Let the AP be a + (a +d)+ (a+2d)+ (a +3d) +....... .................... + a +(n-1)d + a +(n -2)d + a +(n-3)d +a +(n-4)d a + (a +d)+ (a+2d)+ (a +3d) = 56 4d + 6d = 56 since a = 11, d = 2 sum of the last 4 terms = 112 (n-1)d + a +(n -2)d + a +(n-3)d +a +(n-4)d =112 4a + (4n-10)d = 112 plug in a = 11 and d= 2 that gives us n = 11 terms read less
Comments
Dislike Bookmark

Hardworking

11 terms
Comments
Dislike Bookmark

Math Educator for Std.11th ,12th , Engineering Entrance and Degree Level with 11+ Years Experience

number of terms = 11
Comments
Dislike Bookmark

Math analyst

11 + 11+d +11+2d +11+3d = 44 +6d = 56. 6d = 56-44 = 12; d = 2. 11+(n-1)d +11 + (n-2)d + 11 +(n-3)d + 11 + (n-4)d = 112; 44 + (4n - 10)*2 = 112; (4n-10)=(112-44)/2 = 68/2 = 34 4n = 44; n =11. wow!
Comments
Dislike Bookmark

Spoken English, BTech Tuition, C Language, C++ Language, CAD etc., with 4 years of experience

11
Comments
Dislike Bookmark

Maths Teacher

First term is 11.Sum of first 4 terms is 4a+6d=56. That is 44+6d=56.So d=2 Sum of last four terms is 4a+d=4a+(4n-10)d=112 (4n-10)2= 112-44=68. 4n-10=34. 4n=44 Hence n=11
Comments
Dislike Bookmark

Mathematics Tutor

Let a = first term, d = common difference and n = number of terms Then, a + a + d + a + 2d + a + 3d = 56 4a + 6d = 56 44 + 6d = 56 (since a = 11) d = 2 Now, 4a + d {(n-1) + (n-2) + (n-3) + (n-4)} = 112 44 + 2 (4n - 10) = 112 4n - 10 = 34 4n = 44 n = 11 Hence, there are 11 terms.
Comments
Dislike Bookmark

View 16 more Answers

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Recommended Articles

Find Class 12 Tuition near you
Class 12 Tuition in Delhi
Class 12 Tuition in Bangalore
Class 12 Tuition in Hyderabad
Class 12 Tuition in Kolkata
Class 12 Tuition in Mumbai
Class 12 Tuition in Chennai
Class 12 Tuition in Pune
Class 12 Tuition in Lucknow
Class 12 Tuition in Jaipur
Class 12 Tuition in Noida
Online Tuition Class 12

Looking for Class 12 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you
X

Looking for Class 12 Tuition Classes?

The best tutors for Class 12 Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class 12 Tuition with the Best Tutors

The best Tutors for Class 12 Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more

ThinkVidya Learning Pvt Ltd © 2010-2025 All Rights Reserved