Using Recursive/Explicit

Front

What is a recursive formula?

Back

A recursive formula defines the terms of a sequence using previous terms. For example, in a geometric sequence, a_n = a_(n-1) * r, where r is the common ratio.

Front

What is an explicit formula?

Back

An explicit formula defines the nth term of a sequence directly in terms of n. For example, in a geometric sequence, a_n = a_1 * r^(n-1).

Front

What does a_1 represent in a sequence?

Back

a_1 represents the first term of the sequence.

Front

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

Back

The common ratio (r) is found by dividing any term by the previous term, r = a_n / a_(n-1).

Front

What is the explicit formula for the geometric sequence 2, 6, 18, 54...?

Back

The explicit formula is a_n = 2 * 3^(n-1).

Front

What is the recursive formula for the sequence 5, 10, 20, 40...?

Back

The recursive formula is a_n = 2 * a_(n-1), with a_1 = 5.

Front

What is the formula to find the nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence is given by a_n = a_1 + (n-1)d, where d is the common difference.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference (d) is the difference between consecutive terms, calculated as d = a_n - a_(n-1).

Front

How do you identify a geometric sequence?

Back

A geometric sequence is identified by a constant ratio between consecutive terms.

Front

What is the first term of the sequence defined by a_n = 3(-4)^(n-1)?

Back

The first term (a_1) is 3.