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Arithmetic Progression EXERCISE 5.4 (Optional)* Solutions
- Q1: Which term of the AP : 121, 117, 113, . . ., is its first negative term? [Hint : Find $n$ for $a_n < 0$]
- Q2: The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
- Q3: A ladder has rungs 25 cm apart. (see Fig. 5.7). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and the bottom rungs are $2\frac{1}{2}$ m apart, what is the length of the wood required for the rungs? [Hint : Number of rungs = $\frac{250}{25} + 1$]
- Q4: The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of $x$ such that the sum of the numbers of the houses preceding the house numbered $x$ is equal to the sum of the numbers of the houses following it. Find this value of $x$. [Hint : $S_{x – 1} = S_{49} – S_x$]
- Q5: A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of $\frac{1}{4}$ m and a tread of $\frac{1}{2}$ m. (see Fig. 5.8). Calculate the total volume of concrete required to build the terrace. [Hint : Volume of concrete required to build the first step = $\frac{1}{4} \times \frac{1}{2} \times 50 m^3$]
Other Exercises for CBSE - Class 10 Mathematics Arithmetic Progression
Chapters in CBSE - Class 10 Mathematics
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Top Tutor 
Little Mount Saidapet, Chennai 
Less than a yr Exp 
5 students 
316 hrs of classes completed 
400 per hour 
Online Classes CBSE Class 9 & 10 Math Expert | CEG & XLRI Alumnus | Multilingual Instruction About Me: High-quality mentorship matters most during the crucial transition of Classes 9 and 10. I am an engineer from College of Engineering, Guindy (1989) and a management alumnus from XLRI Jamshedpur (2004). What I Offer: Targeted CBSE Focus: Specialized coaching for 9th and 10th-grade Math to ensure top board exam results. Global Teaching Standards: Experienced in delivering high-impact math tutoring for students in North America (NAM) Multilingual Comfort: Instruction available in English, Tamil, Hindi, or Telugu to ensure zero communication barriers. I focus on building core conceptual foundations, rigorous practice, and exam-taking strategies. Let's work together to make Math your child's strongest subject!
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Super Tutor Ashok Nagar D' Souza Layout, Bangalore 13 yrs of Exp 29 students 1056 hrs of classes completed 600 per hour Online Classes 10+ years of experience teaching Mathematics for Grades 10 to 12. Consistent record of 100% academic results. Very friendly and supportive learning environment. Encourages students to ask questions freely and confidently. Strong focus on conceptual clarity and problem-solving skills. Helps students build confidence and excel in Mathematics. Fee structure for one-to-one classes: ₹700 per hour. Group classes: ₹4,000 per month.
Sir clears all my doubts he makes difficult concepts easy to understand he takes Previous year questions which makes it easier to prepare
Top Tutor Bataganj, Patna Sadar 2 yrs of Exp 100 per hour Online Classes I am an experienced Spoken English and Class VI-X subject tutor with two years of experience in teaching. Currently, I am pursuing my bachelor's degree in BA from Magadh University. I can teach students who are in State, International Baccalaureate, CBSE and ICSE Board. My students have improved a lot through my teaching, and I've received five reviews till now with 100% positive feedback. I always try to understand my students and help them overcome their fear of failure in specific subjects like math and science.
Top Tutor Virugambakkam, Chennai 20 yrs of Exp 36 students 1713 hrs of classes completed 500 per hour Online Classes I am R.Vinotha ., M.Sc.,M.Phil.,B.Ed in mathematics.I am the trainer/tutor of this course .I was allotted 12 regular classes for a month.I am using through google meet app for online class and also i am taking mathematics tuition at my home.I will create seperate WhatApp group for my tuition students and communicates to them .I will send the class notes to them after completing the class .My class planner is us following: Regular classes : Any 3 days for a week Class duration : 1 hour Home works: Daily write two problems and send it to be in WhatsApp group Test: Daily test : Formulae test: Everyday i am asking 10 formulae through voice message in WhatsApp group after getting my message ,the students will answer the questions and send it tome via tuition group Problems test:Daily write two problems Regular test : Every saturday and sunday Monthly test : Every month fourth saturday doubts clarification time : Every day 7 pm -8 pm I will correct the test papers immedietly and send it to their personal windows and also resolve the students mistakes. Chapter's quiz : After completing every chapters ,i will conduct mathematical quiz for that chapters Revisions: I will revise previous years questio papers After this type of my coachings many of my students got 100 marks in theire board examination .I put lots of efforts to my students and they getting good marks in the board examination .My teaching type is friendly manner.I gave extra solved questions and answers to my students .
Taking class as well as gives coaching in different approaches that can be dealt with the topic thro variety in problems and helps to reach solution with clarity of the nuances to be careful with.
Top Tutor Mohali SAS Nagar, Chandigarh 15 yrs of Exp 18 students 1102 hrs of classes completed 500 per hour Online Classes 
Tutor's home I have more than 15 years of experience in teaching maths and science for class 10 .. I also prepare students for various competition exams like olympiads, NDA etc
She teaches better than every teacher she does conceptual clarity and gives more homework for practice and she helps me to give occasional tests to improve my score
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