Explicit 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 common difference in a sequence?

Back

Subtract the first term from the second term (d = a2 - a1).

Front

What is the explicit formula for an arithmetic sequence?

Back

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

Front

Given the sequence 3, 7, 11, 15, what is the common difference?

Back

The common difference is 4.

Front

Write the explicit rule for the arithmetic sequence 5, 10, 15, 20,...

Back

a_n = 5n.

Front

Is the sequence 10, 7, 4, 1, ... arithmetic?

Back

Yes, it is arithmetic with a common difference of -3.

Front

What is the explicit rule for the arithmetic sequence 0, 2, 4, 6,...?

Back

a_n = 2n.

Front

Determine the common difference for the sequence 8, 5, 2, -1,...

Back

The common difference is -3.

Front

Write the explicit rule for the arithmetic sequence 1, 4, 7, 10,...

Back

a_n = 3n - 2.