Unit 7 - Sequences and Comparing

Front

What is the formula to find the nth term of an arithmetic sequence?

Back

a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

How do you find the common difference in an arithmetic sequence?

Back

Subtract the first term from the second term (d = a_2 - a_1).

Front

What is a geometric sequence?

Back

A sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

How do you find the next term in a geometric sequence?

Back

Multiply the last term by the common ratio (next term = last term * r).

Front

What is the common ratio in a geometric sequence?

Back

The factor by which we multiply to get from one term to the next (r = a_2 / a_1).

Front

What type of function is represented by a linear relationship?

Back

A linear function has a constant rate of change and can be represented by the equation y = mx + b.

Front

What is the difference between linear and quadratic functions?

Back

Linear functions have a constant slope, while quadratic functions have a variable slope and are represented by y = ax^2 + bx + c.

Front

How can you identify a linear function from a set of data points?

Back

If the differences between consecutive y-values are constant, the function is linear.

Front

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

Back

a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What does it mean for a sequence to be arithmetic?

Back

In an arithmetic sequence, the difference between consecutive terms is constant.