Exponential and Arithmetic Sequences

This video covers AP precalculus topics 2.1 to 2.8, including arithmetic and geometric sequences, linear and exponential functions, and their applications. It explains how to find the nth term, graph sequences, and convert them into functions. The video also discusses the properties of exponents and logs, residual plots, function compositions, and inverse functions. Practical applications of these concepts are demonstrated through real-world examples.

What is the common difference in an arithmetic sequence where each term increases by 3?

• 2

• 1

• 4

• 3

In a geometric sequence, if the first term is 1 and the common ratio is 3, what is the third term?

• 81

• 3

• 9

• 27

Which formula is used to find the nth term of an arithmetic sequence when the first term is known?

• a_n = a_0 * r^n

• a_n = a_k * r^(n-k)

• a_n = a_k + d*(n-k)

• a_n = a_0 + n*d

How do you determine if a sequence is neither arithmetic nor geometric?

• Check if it has both a common difference and a common ratio

• Check if it has neither a common difference nor a common ratio

• Check if it has a common ratio

• Check if it has a common difference

What is the common ratio in a geometric sequence where each term is multiplied by -2?

• 1/2

• -2

• 2

• -1/2

If a sequence is converted to a linear function, what characteristic does it exhibit?

• Constant rate of change

• No change

• Exponential growth

• Exponential decay

What happens to an exponential function when the base is between 0 and 1?

• It decays

• It grows

• It oscillates

• It remains constant

How can you rewrite an exponential function using logs?

• By using the properties of logs

• By dividing exponents

• By adding exponents

• By multiplying exponents

What does a clear pattern in a residual plot indicate?

• A good fit

• A poor fit

• No fit

• An exact fit

In compositions of functions, which function do you evaluate first?

• The outer function

• The inner function

• Both simultaneously

• Neither