Arithmetic Sequences - Explicit Formulas

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

What is the explicit formula for the arithmetic sequence 5, 8, 11, ...?

Back

The explicit formula is a_n = 5 + 3(n - 1).

Front

Find the 22nd term of the sequence 5, 8, 11, ...

Back

The 22nd term is 68.

Front

What is the explicit formula for the sequence -3, -33, -63, -93, ...?

Back

The explicit formula is a_n = -3 - 30(n - 1).

Front

How do you determine the common difference from a sequence?

Back

Subtract any term from the subsequent term. For example, in the sequence 34, 37, 40, 43, the common difference is 3.

Front

What is the 15th term of the sequence a_n = -3n + 50?

Back

The 15th term is 5.

Front

What is the formula to find the nth term of the sequence 34, 37, 40, 43, ...?

Back

The formula is a_n = 34 + 3(n - 1).

Front

How do you find the 32nd term of the sequence 34, 37, 40, 43, ...?

Back

The 32nd term is 127.