Flashcard 1.1 Arithmetic Sequences B

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 explicit formula for an arithmetic sequence?

Back

The explicit formula for an arithmetic sequence can be found using the formula: a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference.

Front

What is the recursive formula for an arithmetic sequence?

Back

The recursive formula for an arithmetic sequence is given by: a_1 = first term, a_n = a_{n-1} + d.

Front

Given the sequence -3, -33, -63, -93, what is the common difference?

Back

The common difference is -30.

Front

What is the explicit formula for the sequence 22, 17, 12, 7?

Back

The explicit formula is a_n = -5n + 27.

Front

How do you determine the first term of an arithmetic sequence from its recursive formula?

Back

The first term is given as a_1 in the recursive formula.

Front

What is the explicit formula for the sequence 7, 27, 47, 67?

Back

The explicit formula is f(x) = 20x - 13.

Front

If a_1 = 2 and a_n = a_{n-1} + 3, what is the second term a_2?

Back

a_2 = a_1 + 3 = 2 + 3 = 5.

Front

What is the difference between explicit and recursive formulas?

Back

An explicit formula gives the nth term directly, while a recursive formula defines each term based on the previous term.