# ARITHMETIC PROGRESSIONS CLASS 10

Get Complete Syllabus of Chapter 5 Arithmetic Progressions Class 10 Maths :

NCERT Exercise 5.1

NCERT Exercise 5.2

NCERT Exercise 5.3

NCERT Chapter 5 Examples

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Subject Language: ENGLISH

Explanation Language: HINDI (HINGLISH)

## Lecture – 1

00:00:00 Meaning of Sequences & Series

00:02:37 Meaning of Arithmetic Progression, first term, common difference, nth term, general term

00:10:37 NCERT Exercise 5.1 Question 2

00:13:17 NCERT Exercise 5.1 Question 3

00:15:57 NCERT Exercise 5.1 Question 4

00:32:45 NCERT Exercise 5.1 Question 1 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.

(ii) The amount of air present in a cylinder when a vacuum pump removes 1/4 of the air remaining in the cylinder at a time.

(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.

(iv) The amount of money in the account every year, when ₹ 10000 is deposited at compound interest at 8 % per annum.

## Lecture – 2

00:05:24 NCERT Exercise 5.2 Question 1

00:12:24 NCERT Exercise 5.2 Question 2

00:15:34 NCERT Exercise 5.2 Question 3

00:31:04 NCERT Exercise 5.2 Question 4 Which term of the AP : 3, 8, 13, 18, . . . ,is 78?

00:34:24 NCERT Exercise 5.2 Question 5

00:42:17 NCERT Exercise 5.2 Question 6 Check whether – 150 is a term of the AP : 11, 8, 5, 2 . . .

00:46:57 NCERT Exercise 5.2 Question 7 Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

00:52:07 NCERT Exercise 5.2 Question 8 An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

00:57:47 NCERT Exercise 5.2 Question 10 The 17th term of an AP exceeds its 10th term by 7. Find the common difference.

## Lecture – 3

00:01:12 NCERT Exercise 5.2 Question 11 Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?

00:06:32 NCERT Exercise 5.2 Question 12 Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?

00:11:52 NCERT Exercise 5.2 Question 13 How many three-digit numbers are divisible by 7?

00:25:52 NCERT Exercise 5.2 Question 14 How many multiples of 4 lie between 10 and 250?

00:31:22 NCERT Exercise 5.2 Question 15 For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?

00:36:32 NCERT Exercise 5.2 Question 16 Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.

## Lecture – 4

00:02:03 NCERT Exercise 5.2 Question 17 Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.

00:06:23 NCERT Exercise 5.2 Question 18 The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

00:11:03 NCERT Exercise 5.2 Question 19 Subba Rao started work in 1995 at an annual salary of ₹5000 and received an increment of ₹200 each year. In which year did his income reach ₹ 7000?

00:15:53 NCERT Exercise 5.2 Question 20 Ramkali saved ₹ 5 in the first week of a year and then increased her weekly savings by ₹ 1.75. If in the nth week, her weekly savings become ₹ 20.75, find n.

## Lecture – 5

00:00:55 Meaning and derivation of rule for Sum to n terms of an AP

00:15:47 Difference between general term and sum to n terms of an AP

00:17:34 NCERT Exercise 5.3 Question 1

00:26:14 NCERT Exercise 5.3 Question 2

00:36:54 NCERT Exercise 5.3 Question 3 part (i) (ii) (iii)

## Lecture – 6

00:00:05 Difference in uses of general term and sum to n terms rule

00:09:33 NCERT Exercise 5.3 Question 3 part (iv) (v) (vi) (vii) (viii) (ix) (x)

00:40:33 NCERT Exercise 5.3 Question 4 How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?

00:47:03 NCERT Exercise 5.3 Question 5 The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

00:49:03 NCERT Exercise 5.3 Question 6 The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

00:52:33 NCERT Exercise 5.3 Question 7 Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

## Lecture – 7

00:03:44 NCERT Exercise 5.3 Question 8 Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

00:06:34 NCERT Exercise 5.3 Question 9 If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

00:13:14 NCERT Exercise 5.3 Question 10

00:24:04 NCERT Exercise 5.3 Question 11 If the sum of the first n terms of an AP is 4n-n^2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

00:31:24 NCERT Exercise 5.3 Question 12 Find the sum of the first 40 positive integers divisible by 6.

00:34:14 NCERT Exercise 5.3 Question 13 Find the sum of the first 15 multiples of 8.

00:35:54 NCERT Exercise 5.3 Question 14 Find the sum of the odd numbers between 0 and 50.

00:38:54 NCERT Exercise 5.3 Question 15 A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ 200 for the first day, ₹ 250 for the second day, ₹ 300 for the third day, etc., the penalty for each succeeding day being ₹ 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?

00:43:42 NCERT Exercise 5.3 Question 16 A sum of ₹ 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ 20 less than its preceding prize, find the value of each of the prizes.

## Lecture – 8

00:00:59 NCERT Exercise 5.3 Question 17 In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?

00:04:23 NCERT Exercise 5.3 Question 18 A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown in Fig. 5.4. What is the total length of such a spiral made up of thirteen consecutive semicircles?

00:12:43 NCERT Exercise 5.3 Question 19 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on (see Fig. 5.5). In how many rows are the 200 logs placed and how many logs are in the top row?

00:19:43 NCERT Exercise 5.3 Question 20 In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line (see Fig. 5.6). A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

00:25:13 NCERT Optional Exercise 5.4 Question 1 Which term of the AP : 121, 117, 113, . . ., is its first negative term?