Ex 5.3 Q17 - 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?
Solution:- *The number of trees, that each section of each class will plant, will be the same as the class, in which they are studying,
*A section of Class I will plant 1 tree
*A section of Class II will plant 2 trees
*There are three sections of each class
Therefore,
*Trees planted by Class I = 1 × 3 = 3
*Trees planted by Class II = 2 × 3 = 6
*Trees planted by Class III = 3 × 3 = 9
.
.
*Trees planted by Class XlI = 12 × 3 = 36
*So, trees planted by Classes l, ll, lll, ... Xll are 3, 6, 9, ... , 36
*Clearly this forms an AP with,
a = 3 d = 3
∵ There are total 12 classes,
∴ n = 12
➙ Total number of trees planted
= Sum of trees planted by each class
= 3 + 6 + 9 + ... + 36
= S₁₂
*Using formula, Sₙ =
n
/
2
[2a + (n - 1)d] =
12
/
2
[2(3) + (12 - 1)3] = 6[6 + (11)3]
= 6(6 + 33)
= 6(39)
= 234
Hence,
Total 234 trees will be planted by the students.
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Try This..
✒ A student scores 10 marks in the first test and increases it by 2 marks in each subsequent test. What is the total score in 5 tests?
✒ The 10th term of an AP is 50. If the first term is 5, find the common difference.
✒ Find the sum of the first 20 terms of the AP: 2, 4, 6, 8...
✒ How many terms are there in the AP 3, 6, 9, ..., 99?
❌ Common Mistakes
▸ Forgetting to multiply by 3 sections – A common mistake!▸ Misidentifying the first term (a) and the last term (l).▸ Using wrong values in the AP formula (especially the number of terms n).▸ Confusing between AP sum formula and nth term formula.
📝 Related Questions:-
- Ex 5.3 Q4 - How many terms of the AP: 9, 17, 25,... must be taken to give a sum of 636?
- Ex 5.3 Q5 - 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.
- Ex 5.3 Q6 - 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?
- Ex 5.3 Q15 - 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?
- Ex 5.3 Q16 - 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.
Queries Solved:-
Class 10 Ex 5.3
Ex 5.3 Q17 Class 10
Class 10 Ex 5.3 Q17
Class 10 Chap 5 Ex 5.3 Q17
Class 10 Arithmetic Progression
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