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 and d is the common difference.

Front

Given the first term 4 and common difference 3, what is the 5th term?

Back

The 5th term is 4 + (5-1)3 = 4 + 12 = 16.

Front

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

Back

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

Front

If the first term is 10 and the common difference is -2, what are the first four terms?

Back

The first four terms are 10, 8, 6, 4.

Front

Identify the common difference in the sequence: 5, 8, 11, 14.

Back

The common difference is 3.

Front

What is the 7th term of the sequence defined by the recursive rule a_n = a_(n-1) + 4, with a_1 = 2?

Back

The 7th term is 26.

Front

If the sequence is 1, 5, 9, 13, what is the common difference?

Back

The common difference is 4.

Front

Find the next two terms of the sequence: 12, 15, 18, 21.

Back

The next two terms are 24 and 27.