INT 3 - Lesson 6.5

Front

What is the explicit formula for a linear sequence?

Back

An explicit formula for a linear sequence is a formula that allows you to find the nth term directly, typically in the form of C(n) = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

Front

What does 'n' represent in an explicit formula?

Back

In an explicit formula, 'n' represents the term number in the sequence.

Front

How do you find the first term of a sequence using an explicit formula?

Back

To find the first term of a sequence using an explicit formula, substitute n=1 into the formula.

Front

What is a common difference in a linear sequence?

Back

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

Front

How do you simplify the expression C(n) = 9 - 4(n - 1)?

Back

Distributing -4 gives C(n) = 9 - 4n + 4, which simplifies to C(n) = 13 - 4n.

Front

What is the significance of a negative common difference?

Back

A negative common difference indicates that the sequence is decreasing.

Front

What is the first term in the sequence when n=1 for the formula C(n) = 13 - 4n?

Back

When n=1, C(1) = 13 - 4(1) = 9.

Front

What happens to the sequence if the common difference is zero?

Back

If the common difference is zero, all terms in the sequence are the same, resulting in a constant sequence.

Front

How do you handle a negative common difference in the explicit formula?

Back

You add it as a negative number, which effectively subtracts from the previous term.

Front

What is the result of distributing -4 in the formula -4(n - 1)?

Back

The result is -4n + 4.