7.1-7.2 Flashcard Review

Front

What is a recursive rule in mathematics?

Back

A recursive rule defines the terms of a sequence using previous terms. It typically includes a starting value and a formula to find subsequent terms.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term increases or decreases by in an arithmetic sequence.

Front

Write the recursive formula for the sequence 45, 49, 53, 57, 61.

Back

f(1) = 45, f(n) = f(n - 1) + 5.

Front

What is the first term of the sequence defined by a_n = 19 - 5(n-1)?

Back

The first term is 19.

Front

How do you find the sum of the first n terms of an arithmetic sequence?

Back

The sum can be found using the formula S_n = n/2 * (a₁ + a_n), where a₁ is the first term and a_n is the nth term.

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula is a_n = a₁ + (n - 1)d, where a₁ is the first term and d is the common difference.

Front

Given the sequence 15, 12, 9, 6, 3, what is the recursive formula?

Back

a₁ = 15, a_n = a_n-1 - 3.

Front

What is the common difference of the sequence where the landscaper installs 24 feet on the first day and 12 feet on each subsequent day?

Back

The common difference is 12 feet.

Front

Calculate the sum of the first 5 terms of the sequence 5, 11, 17, 23.

Back

The sum is 85.

Front

What does it mean for a sequence to be arithmetic?

Back

A sequence is arithmetic if the difference between consecutive terms is constant.