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 explicit formula for an arithmetic sequence?

Back

The explicit formula for an arithmetic sequence is given by a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference.

Front

How do you find the common difference in an arithmetic sequence?

Back

The common difference (d) is found by subtracting any term from the subsequent term, d = a_(n+1) - a_n.

Front

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

Back

The common difference is 3.

Front

What is the first term of the sequence a_n = 5 + 3(n - 1)?

Back

The first term is 5.

Front

Find the explicit formula for the sequence: 4, 10, 16, 22, ...

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a_n = 4 + 6(n - 1).

Front

What is the 10th term of the sequence a_n = 2n + 3?

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The 10th term is 23.

Front

Given the sequence: 10, 7, 4, 1, ... write the explicit formula.

Back

a_n = 10 - 3(n - 1).

Front

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

Back

You can determine the nth term using the formula a_n = a_1 + (n - 1)d.

Front

What is the explicit formula for the sequence: -5, -2, 1, 4, ...?

Back

a_n = -5 + 3(n - 1).