Find the best tutors and institutes for Class 10 Tuition
Q2(i):
Write first four terms of the AP, when the first term $a$ and the common difference $d$ are given as follows:
(i) $a = 10, d = 10$
Solution :
Given: The first term of the Arithmetic Progression (AP), denoted by $a = 10$, and the common difference, denoted by $d = 10$.
To Find: The first four terms of the Arithmetic Progression ($a_1, a_2, a_3, a_4$).
Theoretical Context: An Arithmetic Progression is a sequence of numbers such that the difference between consecutive terms is constant. This constant is called the common difference ($d$). The general form of an AP is given by $a, a+d, a+2d, a+3d, \dots$.
Step 1: Defining the terms of the AP
Let the terms of the AP be represented as $a_n$, where $n$ is the position of the term in the sequence. The formula for the $n$-th term is:
$a_n = a + (n - 1)d$
Step 2: Calculating the first term ($a_1$)
By definition, the first term is $a$.
$a_1 = a$
Substituting the given value $a = 10$:
$a_1 = 10$
Step 3: Calculating the second term ($a_2$)
Using the definition of an AP, the second term is the sum of the first term and the common difference:
$a_2 = a_1 + d$
Substituting the values $a_1 = 10$ and $d = 10$:
$a_2 = 10 + 10$
$a_2 = 20$
Step 4: Calculating the third term ($a_3$)
The third term is the sum of the second term and the common difference:
$a_3 = a_2 + d$
Substituting the values $a_2 = 20$ and $d = 10$:
$a_3 = 20 + 10$
$a_3 = 30$
Step 5: Calculating the fourth term ($a_4$)
The fourth term is the sum of the third term and the common difference:
$a_4 = a_3 + d$
Substituting the values $a_3 = 30$ and $d = 10$:
$a_4 = 30 + 10$
$a_4 = 40$
Summary of Results:
The first four terms are $10, 20, 30, 40$.
Final Answer: The first four terms of the AP are 10, 20, 30, and 40.
More Questions from Class 10 Mathematics Arithmetic Progression EXERCISE 5.1
- Q1(i): In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? (i) The taxi fare after each km when the fare is ₹ 15 for the first km and ₹ 8 for each additional km.
- Q1(ii): In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? (ii) The amount of air present in a cylinder when a vacuum pump removes $\frac{1}{4}$ of the air remaining in the cylinder at a time.
- Q1(iii): In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? (iii) The cost of digging a well after every metre of digging, when it costs ₹ 150 for the first metre and rises by ₹ 50 for each subsequent metre.
- Q1(iv): In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? (iv) The amount of money in the account every year, when ₹ 10000 is deposited at compound interest at 8 % per annum.
- Q2(ii): Write first four terms of the AP, when the first term $a$ and the common difference $d$ are given as follows: (ii) $a = –2, d = 0$
- Q2(iii): Write first four terms of the AP, when the first term $a$ and the common difference $d$ are given as follows: (iii) $a = 4, d = – 3$
- Q2(iv): Write first four terms of the AP, when the first term $a$ and the common difference $d$ are given as follows: (iv) $a = – 1, d = \frac{1}{2}$
- Q2(v): Write first four terms of the AP, when the first term $a$ and the common difference $d$ are given as follows: (v) $a = – 1.25, d = – 0.25$
- Q3(i): For the following APs, write the first term and the common difference: (i) 3, 1, – 1, – 3, . . .
- Q3(ii): For the following APs, write the first term and the common difference: (ii) – 5, – 1, 3, 7, . . .
- Q3(iii): For the following APs, write the first term and the common difference: (iii) $\frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3}, . . .$
- Q3(iv): For the following APs, write the first term and the common difference: (iv) 0.6, 1.7, 2.8, 3.9, . . .
- Q4(i): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (i) 2, 4, 8, 16, . . .
- Q4(ii): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (ii) $2, \frac{5}{2}, 3, \frac{7}{2}, . . .$
- Q4(iii): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (iii) – 1.2, – 3.2, – 5.2, – 7.2, . . .
- Q4(iv): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (iv) – 10, – 6, – 2, 2, . . .
- Q4(ix): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (ix) 1, 3, 9, 27, . . .
- Q4(v): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (v) $3, 3+\sqrt{2}, 3+2\sqrt{2}, 3+3\sqrt{2}, . . .$
- Q4(vi): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (vi) 0.2, 0.22, 0.222, 0.2222, . . .
- Q4(vii): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (vii) 0, – 4, – 8, –12, . . .
- Q4(viii): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (viii) $-\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, . . .$
- Q4(x): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (x) $a, 2a, 3a, 4a, . . .$
- Q4(xi): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (xi) $a, a^2, a^3, a^4, . . .$
- Q4(xii): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (xii) $\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, . . .$
- Q4(xiii): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (xiii) $\sqrt{3}, \sqrt{6}, \sqrt{9}, \sqrt{12}, . . .$
- Q4(xiv): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (xiv) $1^2, 3^2, 5^2, 7^2, . . .$
- Q4(xv): Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (xv) $1^2, 5^2, 7^2, 73, . . .$
CBSE Solutions for Class 10 Mathematics Arithmetic Progression
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Arithmetic Progression
Top Tutor
Sardar Patel Nagar, Dhanbad
6 yrs of
Exp
60 hrs of classes completed
Online Classes
I am an experienced, qualified teacher and tutor with over 5 years of experience in teaching Maths and phy , across different boards and diffrent entrance exam including IIT-JEE , Neet ,B.tech. Passionate about solving mathematical problems and physics problem, over the years I have helped thousands of students overcome their fear of Maths and physics.
Top Tutor
Mira Road, Mira-Bhayandar
10 yrs of
Exp
7 students
84 hrs of classes completed
600
per hour
Student's Home
Tutor's home
Math and physics teacher. Expert in cbse education and assessment patten. Been an cbse examiner for 5 continuous years. Aware of the curriculum of ssc, icse and cbse grade 7-10 math and physics. Tutoring since 2006 and been quite successful in giving results.
Top Tutor
Electronic City Electronics City Phase 1, Bangalore
15 yrs of
Exp
5 students
39 hrs of classes completed
1000
per hour
Online Classes
Ph.D enrolled, M.Tech(Electrical eng). Over 15 years of experience in teaching at different Engineering colleges and tutoring across different boards including CBSE, ICSE, IGCSE, IBDP, Level AS/A in Mathematics & Science. Approachable to students & succeeded to boost their fundamental knowledge.
Ms. Dipika always ensures that students are thorough with the concepts and discourages mugging the formulae. She is chill with students; she actively helps and encourages students to perform their best rather than nagging them about a poor performance. Her teaching methods are simple, effective and logical. It helps build a strong conceptual foundation for advanced topics. Overall, Ms. Dipika is the perfect Maths tutor!
Top Tutor
Nehru Nagar, Belgaum
2 yrs of
Exp
9 students
203 hrs of classes completed
260
per hour
Online Classes
I teach Mathematics to students from Class 7 to Class 10, with 3 years of teaching experience. My focus is on helping students build strong conceptual understanding and develop effective problem-solving skills to excel academically. I have completed my 2nd PUC (Pre-University Course), a Bachelor of Engineering (B.E.) from Visveswaraya Technological University in 2020, and a Bachelor of Education (B.Ed.) from Indira Gandhi National Open University in 2022. I have also completed a program with Cambridge Learning Resources, which has enhanced my teaching techniques and ability to engage students effectively. Over the years, I have guided students to improve their Mathematics understanding and performance, helping them gain confidence in handling both basic and complex problems. My teaching approach emphasizes clarity, practice, and logical reasoning to ensure steady improvement. I have also earned an RPA (Robotic Process Automation) certification in robotics, which reflects my technical skills and commitment to continuous learning. I often incorporate logical thinking and problem-solving strategies inspired by this training into my lessons. I prefer to conduct online classes, offering flexibility in timing and easy access for students. I teach both individual and small group sessions, allowing personalized attention and interactive learning experiences for every student. My classes are interactive, using motivational videos, personal digital pads, and other digital tools to make learning engaging and effective. These resources help students visualize concepts better and retain knowledge more efficiently. I provide custom-prepared notes to support student learning and revision. My ultimate goal is to make Mathematics understandable, enjoyable, and confidence-building, enabling every student to perform at their best and develop a strong foundation for future studies.
This guy is too good at his teaching. He explains the concepts very clear, gets to know about the students, gives his own ideas, own methods, and also gives good advices. He is excellent to consider. I just like him!, he is a great tutor and price is reasonably good.
Top Tutor
Kharodi West, Mumbai
10 yrs of
Exp
1 student
700
per hour
Student's Home
An accommodating and versatile individual with the talent to develop inspiring hands-on lessons that will capture a child's imagination and breed success.
Find more Tutor for Arithmetic Progression in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
Download free CBSE - Class 10 Mathematics Arithmetic Progression EXERCISE 5.1 worksheets
Download Now
