2.3 Algebra 1 Recap

Front

What is an explicit formula for an arithmetic sequence?

Back

An explicit formula for an arithmetic sequence is a formula that allows you to find the nth term of the sequence using the first term and the common difference. It is generally expressed as 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 in an arithmetic sequence is found by subtracting any term from the subsequent term. For example, in the sequence 10, 20, 30, 40, the common difference is 20 - 10 = 10.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

How do you find the common ratio in a geometric sequence?

Back

The common ratio in a geometric sequence is found by dividing any term by the previous term. For example, in the sequence 2, 4, 8, 16, the common ratio is 4 / 2 = 2.

Front

What is the formula for the nth term of a geometric sequence?

Back

The formula for the nth term of a geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

Is the sequence 5, 4.25, 3.5, 2.75 an arithmetic sequence?

Back

Yes, it is an arithmetic sequence because the difference between consecutive terms is constant (each term decreases by 0.75).

Front

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

Back

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

Front

How do you determine if a sequence is arithmetic?

Back

To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant.

Front

What is the 32nd term of the sequence 9, 4, -1, -6, -11?

Back

The 32nd term is -146.

Front

What is the common difference in the sequence 10, 20, 30, 40?

Back

The common difference is 10.