Arithmetic Progression

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What is the formula for the nth term of an arithmetic progression?

The formula is a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.

How do you find the common difference in an arithmetic sequence?

Subtract the first term from the second term: d = a_2 - a_1.

How do you calculate the sum of the first n terms in an arithmetic sequence?

The sum is given by S_n = n/2 * (2a_1 + (n - 1)d).

What is the sum of the first 10 terms if the first term is 5 and the common difference is 3?

The sum is 185.

If the common difference in a sequence is negative, what does this indicate?

It indicates that the sequence is decreasing.

Can the terms of an arithmetic progression be identical?

Yes, if the common difference is zero.

What do you call an arithmetic sequence with only two numbers?

A 2-term arithmetic sequence.

How is an arithmetic progression different from a geometric progression?

Arithmetic progression adds a constant (common difference), while geometric progression multiplies by a constant (common ratio).

What happens to an arithmetic sequence if all terms are multiplied by a constant?

The sequence remains arithmetic with a scaled common difference.

How is the midpoint of an arithmetic sequence found?

The midpoint is the average of the first and last terms.

If the 5th term of an arithmetic progression is 15 and the 7th term is 21, what is the common difference?

The common difference is 3.

What is the general form of an arithmetic sequence?

It's expressed as: a_1, a_1+d, a_1+2d, ..., a_1+(n-1)d.

How can you verify if a given sequence is arithmetic?

Check if the difference between consecutive terms is constant.

Can an arithmetic progression be infinite?

Yes, unless restricted, it can continue indefinitely in either direction.

What happens to the mean of an arithmetic sequence if the same number is added to each term?

The mean increases by that number.


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1. What is the formula for the nth term of an arithmetic progression?

The formula is a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.

The formula is a_n = a_1 + n - d.

The formula is a_n = a_1 * d + n.

The formula is a_n = (n - 1) a_1 + nd.

2. How do you find the common difference in an arithmetic sequence?

Add the first term to the second term.

Subtract the first term from the second term: d = a_2 - a_1.

Divide the first term by the second term.

Multiply the first term by the second term.

3. How do you calculate the sum of the first n terms in an arithmetic sequence?

The sum is given by S_n = n/2 * (2a_1 + (n - 1)d).

The sum is given by S_n = a_n * n - d.

The sum is given by S_n = n(a_1 + d).

The sum is given by S_n = (2a_1 + nd)/2.

4. If the common difference in a sequence is negative, what does this indicate?

The sequence has reached its maximum.

It indicates that the sequence is decreasing.

The sequence becomes a geometric progression.

The sequence is undefined.

5. Can the terms of an arithmetic progression be identical?

No, the common difference must be positive.

Yes, if all terms are prime numbers.

Yes, if the common difference is zero.

No, the terms must always differ.

6. What do you call an arithmetic sequence with only two numbers?

A binary arithmetic sequence.

A single-term arithmetic sequence.

A 2-term arithmetic sequence.

A minimal sequence.

7. How is an arithmetic progression different from a geometric progression?

Arithmetic progression adds a constant (common difference), while geometric progression multiplies by a constant (common ratio).

Arithmetic progression divides a constant, while geometric adds a constant.

Arithmetic progression has varying differences, geometric has varying ratios.

Arithmetic multiplies a constant, geometric divides a constant.

8. What happens to an arithmetic sequence if all terms are multiplied by a constant?

The sequence remains arithmetic with a scaled common difference.

The sequence becomes non-arithmetic.

The sequence remains constant.

The sequence turns into a geometric progression.

9. How is the midpoint of an arithmetic sequence found?

The midpoint is the average of the first and last terms.

The midpoint is the first term plus the last term.

The midpoint is the product of the middle two terms.

The midpoint is the term number multiplied by the common difference.

10. What is the general form of an arithmetic sequence?

It's expressed as: a_1, a_1 + d^n, ..., a_1 + n^2 d.

It's expressed as: a_1, a_1+d, a_1+2d, ..., a_1+(n-1)d.

It's expressed as: a_1, a_2, a_3, ..., a_n.

It's expressed as: a_1 + a_2, a_2 + a_3, ..., a_n + a_{n-1}.