Sequences and Exponential Functions Flashcard

Front

Define an arithmetic sequence.

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference (d). For example, in the sequence 3, 6, 9, 12, the common difference is 3.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

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

Tags

CCSS.HSF.BF.A.2

Front

Identify the common difference in the arithmetic sequence 5, 10, 15, 20.

Back

The common difference (d) in the sequence is 5, as each term increases by 5.

Tags

CCSS.HSF.BF.A.2

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent. The base b determines the growth or decay rate.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base (b) of the exponential function is greater than 1 (e.g., f(x) = 2^x), leading to rapid increase. Exponential decay occurs when the base (b) is between 0 and 1 (e.g., f(x) = 0.5^x), leading to rapid decrease.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

The sum (S_n) of the first n terms of an arithmetic sequence can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio (r). For example, in the sequence 2, 6, 18, 54, the common ratio is 3.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term (a_n) of a geometric sequence can be calculated using the formula: a_n = a_1 * r^(n - 1), where a_1 is the first term and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

Identify the common ratio in the geometric sequence 3, 9, 27, 81.

Back

The common ratio (r) in the sequence is 3, as each term is multiplied by 3 to get the next term.

Tags

CCSS.HSF.BF.A.2

Front

What transformation is applied to the function f(x) = 5^x to obtain g(x) = 5^{-x}?

Back

The transformation applied is a reflection over the y-axis.

Tags

CCSS.HSF.BF.B.3