Sequences Review

Front

What is a sequence in mathematics?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

Front

Define an arithmetic sequence.

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

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

Back

The nth term can be calculated using the formula: t(n) = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

Front

Define 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.

Front

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

Back

The nth term can be calculated using the formula: t(n) = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.

Front

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

Back

The common difference is found by subtracting any term from the subsequent term.

Front

How do you find the common ratio in a geometric sequence?

Back

The common ratio is found by dividing any term by the previous term.

Front

What is the 22nd term of the arithmetic sequence: 5, 8, 11, ...?

Back

The 22nd term is 68.

Front

If f(x)=2x+17, what is f(12)?

Back

f(12) = 41.

Front

Identify whether the sequence 256, 64, 16, 4 is arithmetic or geometric.

Back

It is a geometric sequence with a common ratio of 1/4.