Arithmetic Progression

The video tutorial introduces arithmetic sequences, explaining how each term is derived by adding a constant, known as the common difference, to the previous term. It covers the graphical representation of arithmetic progressions, showing how they form straight lines on an XY plane. The tutorial also explains how to derive the general term of an arithmetic progression and discusses various properties and operations that can be performed on these sequences. Finally, it demonstrates how to calculate the sum of terms in an arithmetic progression using Gauss's method.

What is the term used to describe the constant added to each term in an arithmetic sequence?

• Common ratio

• Common divisor

• Common difference

• Common factor

How does the graph of an arithmetic progression with a positive common difference appear?

• A horizontal line

• A straight line heading upwards

• A curve

• A straight line heading downwards

If the common difference of an arithmetic progression is zero, what does the graph look like?

• A straight line heading downwards

• A vertical line

• A horizontal line

• A straight line heading upwards

What is the general term of an arithmetic progression if the nth term is given by 3n + 6?

• 3n - 6

• 3n + 6

• 6n + 3

• 6n - 3

If the fourth term of an arithmetic progression is 8 and the common difference is -2, what is the 20th term?

• 24

• 0

• -8

• -24

What happens to an arithmetic progression if a constant is added to each term?

• It becomes a geometric progression

• It remains an arithmetic progression

• It becomes a harmonic progression

• It becomes a quadratic sequence

If each term of an arithmetic progression is multiplied by a constant, what is the effect on the sequence?

• It becomes a quadratic sequence

• It becomes a harmonic progression

• It remains an arithmetic progression

• It becomes a geometric progression

What is the method called that involves reversing and adding terms to find the sum of an arithmetic progression?

• Newton's method

• Gauss's method

• Euler's method

• Fibonacci's method

In the formula for the sum of n terms of an arithmetic progression, what do the terms within the square brackets represent?

• The difference between the first and last terms

• The product of the first and last terms

• The ratio of the first and last terms

• The sum of the first and last terms

How can the sum of n terms of an arithmetic progression be expressed?

• Using only the first term

• Using only the last term

• Using both the first and last terms

• Using the common difference only