Explicit and Recursive Formulas Review

Front

What is an explicit formula?

Back

An explicit formula defines the nth term of a sequence directly in terms of n.

Front

What is a recursive formula?

Back

A recursive formula defines each term of a sequence based on the previous term(s).

Front

Given the sequence 2, 7, 12, 17, what is the common difference?

Back

The common difference is 5.

Front

If a_n = 7 in the sequence 2, 7, 12, 17, what is a_n+1?

Back

a_n+1 = 12.

Front

Write the explicit formula for the sequence 3, 8, 13, 18.

Back

u_n = -2 + 5n.

Front

What are the first four terms of the sequence defined by a_n = 3(4)ⁿ?

Back

The first four terms are 3, 12, 48, 192.

Front

Define a sequence.

Back

A sequence is a set of numbers in a specific order.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term is given by a_n = a₁ + (n-1)d, where d is the common difference.

Front

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

Back

The nth term is given by a_n = a₁ * r^n-1, where r is the common ratio.

Front

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

Back

Subtract the first term from the second term.