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

What is the common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in the sequence.

Front

How do you find the nth term of an arithmetic sequence?

Back

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

Front

Given the sequence 2, 5, 8, 11, what is the common difference?

Back

The common difference is 3.

Front

Is the sequence 4, 10, 16, 22 an arithmetic sequence?

Back

Yes, it is an arithmetic sequence with a common difference of 6.

Front

What is the 10th term of the arithmetic sequence 3, 7, 11, 15?

Back

The 10th term is 39.

Front

If the first term of an arithmetic sequence is 5 and the common difference is 2, what is the 20th term?

Back

The 20th term is 43.

Front

How many terms are in the arithmetic sequence 1, 4, 7, ..., 100?

Back

There are 34 terms.

Front

What is the formula for the sum of the first n terms of an arithmetic sequence?

Back

The sum S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

Given the sequence 10, 7, 4, 1, what is the common difference?

Back

The common difference is -3.