CBSE Class 10-Mathematics: Chapter –5 Arithmetic Progressions Part 15

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Question 6:

A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs. for the first day, Rs for the second day, Rs for the third day, etc., the penalty for each succeeding day being Rs more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by days?

Answer:

Penalty for first day , Penalty for second day

Penalty for third day

It is given that penalty for each succeeding day is more than the preceding day.

It makes it an arithmetic progression because the difference between consecutive terms is constant.

We want to know how much money the contractor has to pay as penalty if he has delayed the work by days.

So, we have an AP of the form terms

First term , Common difference

Applying formula, to find sum of n terms of AP, we get

Therefore, penalty for days is Rs. .

Question 7:

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 two trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?

Answer:

There are three sections of each class and it is given that the number of trees planted by any class is equal to class number.

The number of trees planted by class number of sections

The number of trees planted by class number of sections

The number of trees planted by class number of sections

Therefore, we have sequence of the form terms

To find total number of trees planted by all the students, we need to find sum of the sequence terms.

First term , Common difference and

Applying formula, to find sum of n terms of AP, we get

Question 8:

A small terrace at a football ground comprises of steps each of which is long and built of solid concrete.

Each step has a rise of and a tread of (see figure). Calculate the total volume of concrete required to build the terrace.

Answer:

Volume of concrete required to build the first step, second step, third step, ……. are

Total volume of concrete required

Question 9:

For what value of n are the nth term of the following two AP’s being same and

Answer:

term of term of ,………

Therefore,

Question 10:

Check whether is a term of the list of numbers ?

Answer:

So, is not a term of the given list.