Arithmetic Sequences

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

How do you determine if a sequence is arithmetic?

Back

To determine if a sequence is arithmetic, check if the difference between consecutive terms is the same.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term in the sequence increases or decreases by.

Front

Given the arithmetic sequence 5, 10, 15, what is the common difference?

Back

The common difference is 5.

Front

Find the next term in the arithmetic sequence: 2, 4, 6, 8, ...

Back

The next term is 10.

Front

True or False: The sum of the first n terms of an arithmetic sequence can be calculated using the formula S_n = n/2 * (a + l), where a is the first term and l is the last term.

Back

True.

Front

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

Back

The nth term can be calculated using the formula a_n = a + (n-1)d, where a is the first term and d is the common difference.

Front

If the first term of an arithmetic sequence is 3 and the common difference is 4, what is the 5th term?

Back

The 5th term is 19.

Front

What is the relationship between direct variation and arithmetic sequences?

Back

In direct variation, as one variable increases, the other increases at a constant rate, similar to the constant difference in arithmetic sequences.

Front

How can you identify a non-arithmetic sequence?

Back

A non-arithmetic sequence will have varying differences between consecutive terms.