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 that each term increases or decreases by in an arithmetic 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

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

Back

The sum of the first n terms (S_n) can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

If the first term of an arithmetic sequence is 5 and the common difference is 2, what is the 10th term?

Back

The 10th term is 5 + (10-1) * 2 = 23.

Front

What is the common difference in the sequence 3, 7, 11, 15?

Back

The common difference is 4.

Front

What is the difference between two terms in an arithmetic sequence called?

Back

It is called the common difference.

Front

If the sequence is 10, 15, 20, 25, what will be the 6th term?

Back

The 6th term will be 10 + (6-1) * 5 = 35.

Front

Which of the following is an arithmetic sequence: 2, 4, 6, 8 or 1, 2, 4, 8?

Back

2, 4, 6, 8 is an arithmetic sequence because the difference between consecutive terms is constant (2).

Front

What is the 5th term of the arithmetic sequence 1, 4, 7, 10?

Back

The 5th term is 1 + (5-1) * 3 = 13.