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, 8, 14, what is the common difference?

Back

The common difference is 6, calculated as 8 - 2 or 14 - 8.

Front

What is the explicit formula for the sequence 2, 8, 14?

Back

The explicit formula is a_n = 6n - 4.

Front

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

Back

To find the nth term, use the explicit formula a_n = a_1 + (n - 1)d.

Front

What is 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?

Back

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

Front

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

Back

Use the explicit formula a_n = 34 + 3(n - 1) to find the 32nd term, which is 127.

Front

What is the explicit formula for the sequence 25, 21, 17, 13?

Back

The explicit formula is a_n = -4n + 29.