CBSE Class 10-Mathematics: Chapter – 5 Arithmetic Progressions Part 19 (For CBSE, ICSE, IAS, NET, NRA 2022)

Get top class preparation for CBSE right from your home: fully solved questions with step-by-step explanation- practice your way to success.

Question 5:

logs are stacked in the following manner: logs in the bottom row, in the next row, in the row next to it and so on. In how many rows are the placed and how many logs are in the top row?

Answer:

The number of logs in the bottom row

The number of logs in the next row

The number of logs in the next to next row

Therefore, we have sequence of the form

First term , Common difference

We need to find that how many rows make total of logs.

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

It is a quadratic equation; we can factorize to solve the equation.

We discard because we cannot have more than rows in the sequence. The sequence is of the form:

At most, we can have or a smaller number of rows.

Therefore, which means rows make total number of logs equal to .

We also need to find number of logs in the row.

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

Therefore, there are logs in the topmost row and there are total of rows.

Question 6:

In a potato race, a bucket is placed at the starting point, which is meters from the first potato, and the other potatoes are placed 3 meters 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?

The Total Distance the Competitor Has to Run

Answer:

The distance of first potato from the starting point meters

Therefore, the distance covered by competitor to pick up first potato and put it in bucket meters

The distance of Second potato from the starting point meters

Therefore, the distance covered by competitor to pick up potato and put it in bucket meters

The distance of third potato from the starting point meters

Therefore, the distance covered by competitor to pick up 3rd potato and put it in bucket meters

Therefore, we have a sequence of the form terms

(There are ten terms because there are ten potatoes)

To calculate the total distance covered by the competitor, we need to find:

terms

First term , Common difference

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

Therefore, total distance covered by competitor is equal to meters.