Arithmetic Sequences and Recursive 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 common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in the sequence.

Front

Given the sequence 4, 11, 18, 25, what is a_3?

Back

18

Front

What is a recursive formula?

Back

A recursive formula defines each term of a sequence using the preceding term(s).

Front

Given the recursive formula u_1 = 3 and u_n = u_{n-1} + 2, find the first five terms.

Back

3, 5, 7, 9, 11

Front

Write the recursive formula for the sequence 6, 4, 2, 0, ...

Back

a_1 = 6, a_n = a_{n-1} - 2

Front

What is the first term of the sequence defined by a_n = a_{n-1} - 16, starting with a_1 = 17?

Back

17

Front

Determine the 3rd term of the sequence defined by a_1 = 5 and a_n = 2a_{n-1} - 1.

Back

17

Front

Write a recursive rule for the sequence 17, 1, -15, -31 ...

Back

a_n = a_{n-1} - 16

Front

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

Back

The nth term can be found using the formula a_n = a_1 + (n-1)d, where d is the common difference.