cbse ncert 10th mathematics
chapter 5 arithmetic progressions, exercise 5.3
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?
since there are 3 sections for each class
Total number of trees
= 3*[ 1 + 2 + . . . + 12]
using the formula for sum of n terms of an AP inside the [ ... ]
with n=12 first term a =1 last term L = 12
Sn = (n/2) [a +L]
Total number of trees
= 3*[ 1 + 2 + . . . + 12]
= 3* [ (12/2) [1 +12] ]
=3*[(6)*13]
=234 trees
16. A sum of Rs.700 is to be used to give seven 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.
A sum of Rs.700 is to be used means Sn= 700
given that, there are seven cash prizes so n =7
each prize is Rs.20 less than its preceding prize
means that d =(-20) where the minus sign is used for " less "
if the first term a stands for the first prize.
using the formula for sum of n terms of an AP
Sn = (n/2)*[ 2a + (n-1)d ]
700 = (7/2) * [ 2a + (7-1)(-20) ]
700 = (7/2) * [ 2a -120]
2*700 = 7 [2a - 120]
1400 = 14a -840
1400+840 =14a
2240 = 14a
a = 2240/14
a = 160
first prize = a = Rs.160
second prize =a+d = 160 + (-20) = Rs.140
third prize = a+2d = 160 + 2*(-20) = 160-40=Rs.120
fourth prize = a+3d = 160 + 3*(-20) = Rs.100
fifth prize = a+4d = 160 + 4*(-20) = Rs.80
sixth prize = a+5d = 160 + 5*(-20) = Rs.60
seventh prize =a+6d =160 + 6*(-20) = Rs.40
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ncert cbse 10th mathematics
chapter 5 arithmetic progressions
exercise 5.4 optional exercise
Which term of the AP : 121, 117, 113, . . ., is its first negative term?
2. 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.
3. A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and last rungs are [ 2 and(1/2) ]m apart, what is the length of the wood required for the rungs?
4. 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.
solution5. 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 (1/4) m and a tread of (1/2)m. Calculate the total volume of concrete required to build the terrace.
chapter 5 arithmetic progressions, exercise 5.3
exercise 5.3
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.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?
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 . In how many rows are the 200 logs placed and how many logs are in the top row?
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, . . . What is the total length of such a spiral made up of thirteen consecutive semicircles.
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?
16. A sum of Rs.700 is to be used to give seven 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.
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