Find the best tutors and institutes for Class 10 Tuition
Q2(iii):
Write first four terms of the AP, when the first term $a$ and the common difference $d$ are given as follows:
(iii) $a = 4, d = – 3$
Solution :
Given:
The first term of the Arithmetic Progression (AP), denoted by $a = 4$.
The common difference of the Arithmetic Progression, denoted by $d = -3$.
To Find:
The first four terms of the Arithmetic Progression ($a_1, a_2, a_3, a_4$).
Theoretical Basis:
An Arithmetic Progression is a sequence of numbers such that the difference between any two consecutive terms is constant. This constant is called the common difference ($d$).
The general form of an AP is given by: $a, (a + d), (a + 2d), (a + 3d), \dots$
Where:
- $a_1 = a$
- $a_2 = a + d$
- $a_3 = a + 2d$
- $a_4 = a + 3d$
Step 1: Calculating the first term ($a_1$)
By definition, the first term is simply $a$.
$a_1 = a = 4$
Step 2: Calculating the second term ($a_2$)
Using the formula $a_2 = a + d$:
$a_2 = 4 + (-3)$
$a_2 = 4 - 3$
$a_2 = 1$
Step 3: Calculating the third term ($a_3$)
Using the formula $a_3 = a + 2d$:
$a_3 = 4 + 2(-3)$
$a_3 = 4 + (-6)$
$a_3 = 4 - 6$
$a_3 = -2$
Step 4: Calculating the fourth term ($a_4$)
Using the formula $a_4 = a + 3d$:
$a_4 = 4 + 3(-3)$
$a_4 = 4 + (-9)$
$a_4 = 4 - 9$
$a_4 = -5$
Summary of Terms:
| Term | Calculation | Value |
|---|---|---|
| $a_1$ | $a$ | $4$ |
| $a_2$ | $a + d$ | $1$ |
| $a_3$ | $a + 2d$ | $-2$ |
| $a_4$ | $a + 3d$ | $-5$ |
Final Answer: The first four terms of the Arithmetic Progression are 4, 1, -2, and -5.
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(i): Write first four terms of the AP, when the first term $a$ and the common difference $d$ are given as follows: (i) $a = 10, d = 10$
- 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(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
Mahmoorganj Tulsipur, Varanasi
4 yrs of
Exp
12 students
688 hrs of classes completed
100
per hour
Online Classes
Teaching methodology is such that even weakest students can understand the concept very easily through real life analogy
Great teacher i understand subjects with better clarity now and he teaches great and it sure helped me alot
Super Tutor
Badarpur, Delhi
12 yrs of
Exp
152 students
3806 hrs of classes completed
200
per hour
Online Classes
Tutor's home
Akshay is an excellent teacher. He has taught my son in 10 th standard science , with which he understood the concepts clearly and he also gave so many past question papers for my son to work out, all these made my son score 95 in board exams . I would definitely recommend Akshay for students who want to improve and get good scores in science .
Top Tutor
Indirapuram, Ghaziabad
5 yrs of
Exp
39 hrs of classes completed
Online Classes
I was a working professional .Left my job and started teaching as a tutor. I have been a national level debater . I am a famous teacher amongst my students .
Top Tutor
Flanders, Mount Olive
5 yrs of
Exp
2 students
22 hrs of classes completed
100
per hour
Online Classes
I have volunteer teacher for evidyaloka ..I thought higg school students math and science
Top Tutor
Pandeypur, Varanasi
10 yrs of
Exp
14 students
1976 hrs of classes completed
500
per hour
Online Classes
I am Mathematics teacher teaching in a reputed school.
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
