Arithmetic Progression and Summation of Terms

The video tutorial discusses patterns, focusing on arithmetic progression (AP). It explains how to identify and calculate terms in an AP, using examples like stair steps and bank deposits. The tutorial also covers finding specific terms and summing series in AP, providing formulas for generalization.

What is the pattern observed in the staircase example?

• Each step decreases by 0.5 feet

• Each step increases by 1 foot

• Each step remains the same height

• Each step increases by 0.5 feet

In the bank interest example, how much is added to the amount each year?

• 200 rupees

• 150 rupees

• 100 rupees

• 50 rupees

What is the common difference in the project payment example?

• $15

• $10

• $20

• $5

What is the payment on the 21st day of the project?

• $115

• $110

• $105

• $100

How is the nth term of an arithmetic progression calculated?

• t1 + n + d

• t1 + (n - 1) * d

• t1 - (n - 1) * d

• t1 * n * d

What is the payment on the 30th day of the project?

• $165

• $155

• $160

• $150

What is the total revenue from the project over 30 days?

• $2,475

• $2,450

• $2,500

• $2,400

What is the formula for the sum of an arithmetic series?

• (t1 - tn) * n / 2

• (t1 + tn) * n / 2

• (t1 - tn) * d / 2

• (t1 + tn) * d / 2

What is the first step in finding the sum of an arithmetic series?

• Add the first and last terms

• Determine the number of terms

• Find the common difference

• Calculate the last term

Which formula can be used to find the nth term of an arithmetic progression?

• t1 - (n - 1) * d

• t1 - n * d

• t1 + (n - 1) * d

• t1 + n * d