Unit 11 Day 2

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

Define the first term of a sequence.

Back

The first term of a sequence is the initial value from which the sequence begins, often denoted as a₁.

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

How do you find the nth term of an arithmetic sequence?

Back

The nth term can be found using the formula: aₙ = a₁ + (n-1)d, where a₁ is the first term and d is the common difference.

Front

What is a recursive formula?

Back

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

Front

What is an explicit formula?

Back

An explicit formula provides a direct way to calculate the nth term of a sequence without referring to previous terms.

Front

Given a recursive sequence Aₙ = Aₙ₋₁ + 8, what is the first term if A₁ = 3?

Back

The first term A₁ is 3.

Front

How do you derive an explicit formula from a recursive formula?

Back

To derive an explicit formula, identify the pattern in the recursive definition and express it in terms of n.

Front

What is the formula for the nth term of the sequence defined by a₁ = 9 and aₙ = aₙ₋₁ + 8?

Back

The formula is aₙ = 8n + 1.

Front

If a₁ = 2 and the common difference d = 6, what is a₄?

Back

a₄ = 2 + 3(6) = 20.