CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set 13

SA TYPE

Question. Which term of the AP: \( 23, 21, 19, \dots \) is first negative term? Also, find this term.
Answer: \( 13^{\text{th}} \), -1

Question. How many natural numbers are there between 200 and 500, which are divisible by 7?
Answer: 43

Question. Ragav buys a shop for Rs. 120000. He pays the amount in case and agree to pay the balance in 12 annual installment of Rs. 5000 each if the rate of interest is 12 % and he pays with the installment the interest due on the unpaid amount. find the total cost of shop.
Answer: Rs. 166800.

Question. A thief after committing a theft runs a uniform speed of 50m/minute. After 2 minute, a policeman runs to catch him. He goes 60m in first minute and increases his speed by 5m/minute every succeeding minute. After how many minutes, the police will catch the thief.
Answer: 7 minutes

Question. The sum of the first seven terms of an AP is 182. If its \( 4^{\text{th}} \) and the \( 17^{\text{th}} \) terms are in the ratio 1: 5, find the AP.
Answer: 2, 10, 18, ...

Question. A man is in the habit of drinking daily. Amounts spent on drinking are as follows: Rs. 25, Rs. 40, Rs 55, Rs 70 . . . in successive days. What will be total amount spent by him in 30 successive days? Write any two disadvantages of drinking.
Answer: Rs. 7275

Question. The sum of first \( m \) terms of an AP is \( 4m^2 - m \). If its \( n^{\text{th}} \) term is 107, find the value of \( n \). Also find the \( 21^{\text{st}} \) term of this of this AP.
Answer: \( n = 14 \), 163

Question. If \( k, 2k-1 \) and \( 2k+1 \) are three consecutive terms of an A. P. , then find the value of \( k \).
Answer: 3

Question. In an AP, the sum of its first ten terms is \( -80 \) and the sum its next ten terms is \( -280 \). Find the AP.
Answer: \( 1, -1, -3, -5, \dots \)

Question. Three numbers are in AP. If the sum of these numbers be 27 and the product 648, find the numbers.
Answer: 6, 9, 12 or 12, 9, 6

Question. The \( p^{\text{th}}, q^{\text{th}} \) and \( r^{\text{th}} \) terms of an A.P. are \( a, b \) and \( c \) respectively. Show that \( a(q - r) + b(r-p) + c(p - q) = 0 \)
Answer: [Mathematical Proof]

Question. Find the number of three-digit natural numbers which are divisible by 11.
Answer: 81

Question. The \( 5^{\text{th}} \) term of an AP exceeds its \( 12^{\text{th}} \) term by 14. If its \( 7^{\text{th}} \) term is 4, find the AP.
Answer: 16, 14, 12, 10, ...

Question. Determine the AP whose \( 5^{\text{th}} \) term is 19 and the difference of the \( 8^{\text{th}} \) term from the \( 13^{\text{th}} \) term is 20.
Answer: 3, 7, 11, 15

Long Answer type questions

Question. 200 logs are stacked in following manner . 20 logs in the bottom row , 19 in the next row 18 in the row next to it and so on . how many rows are the 200 logs placed and how many logs are in the top row ?
Answer: total rows 16 and 5 logs placed in top row

Question. Ramkali saves Rs 5 in the first week, of a year and increased her weekly savings by Rs 1.75. If in the \( n^{\text{th}} \) week her weekly savings became Rs 20.75, find \( n \).
Answer: 10

Question. The digits of a positive number of three digits are in A.P. and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number.
Answer: 852

Question. In a school, students decided to plant 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 double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.
Answer: 312

Question. If the sum of the first \( n \) terms of an AP is \( 4n - n^2 \), what is the first term (that is \( S_1 \))? What is the sum of first two terms? What is the second term? Similarly find the \( 3^{\text{rd}} \), the \( 10^{\text{th}} \) and the \( n^{\text{th}} \) terms.
Answer: The first term \( S_1 = 3 \), sum of first two terms \( S_2 = 4 \), the second term is 1, The \( 3^{\text{rd}}, 10^{\text{th}} \), and \( n^{\text{th}} \) terms are -1, -15, and \( 5 - 2n \) respectively

Question. A sum of Rs 1600 is to be used to give ten cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.
Answer: 250, 230, 210, 190, 170, 150, 130, 110, 90, 70

Question. A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every succeeding minute. After how many minutes, the policeman will catch the thief?
Answer: police man catch the thief after 5 minutes

Question. Reshma wanted to save at least Rs 6,500 for sending her daughter to school next year (after 12 months). She saved Rs 450 in the first month and raised her savings by Rs 20 every next month. How much will she be able to save in next 12 months? Will she be able to send her daughter to the school next year?
Answer: Rs 6720

Question. The sum of the third and seventh terms of an A.P. is 40 and the sum of its sixth and 14th terms is 70. Find the sum of the first ten terms of the A.P.
Answer: 215

Question. If sum of first \( n \) terms of an AP is \( 4n - n^2 \) What is the first term What is the sum first two terms? Find \( 10^{\text{th}} \) term, \( 3^{\text{rd}} \) term and \( n^{\text{th}} \) term.
Answer: \( S_1 = 3, S_2 = 4, a_{10}= -15, a_3 = -1 \) and \( n^{\text{th}} \) term \( = 5-2n \)

CASE STUDY QUESTIONS 

India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year.

Question. Find the production during first year.
Answer: Rs 5000

Question. Find the production during 8th year.
Answer: \( (a+7d) = 5000 + 7(2200) = 20400 \)

Question. Find the production during first 3 years.
Answer: \( 5000 + 7200 + 9400 = 21600 \)

Question. In which year, the production is Rs 29,200.
Answer: \( N = 12 \)

Difference = 18200 - 11600 = 6600

Question. Your friend Veer wants to participate in a 200m race. He can currently run that distance in 51 seconds and with each day of practice it takes him 2 seconds less. He wants to do in 31 seconds.

Question. Write first four terms are in AP for the given situation.
Answer: 51, 49, 47, 45, ...

Question. What is the minimum number of days he needs to practice till his goal is achieved.
Answer: 11

Question. How many second takes after \( 5^{\text{th}} \) days.
Answer: 43 seconds

Question. Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of Rs 1,18,000 by paying every month starting with the first instalment of Rs 1000. If he increases the instalment by Rs 100 every month, answer the following:

Question. Find the amount paid by him in 30th installment .
Answer: 3900

Question. Find the amount paid by him in the 30 installments .
Answer: 73500

Question. If total instalments are 40 then amount paid in the last installment?
Answer: 4900

Question. Students of a school 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.

Question. Find the total number of trees planted by the students of the school?
Answer: 234

Question. Find total number of trees planted by primary 1 to 5 class students?
Answer: 45

Question. Find total number of classes ?
Answer: 12

Question. 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. 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?

Question. Find terms of AP formed in above situation
Answer: 10, 16, 22, ...

Question. What is the total distance the competitor has to run?
Answer: 370

Question. Find distance cover after 4 potato drop In the bucket?
Answer: 152 m