Review on Combinations, Sequences, Series

Front

What is a combination?

Back

A selection of items from a larger set where the order does not matter.

Front

What is the formula for combinations?

Back

The formula for combinations is \( \frac{n!}{(n-r)! r!} \) where \( n \) is the total number of items and \( r \) is the number of items to choose.

Front

What does \( \binom{10}{5} \) mean?

Back

It represents the number of ways to choose 5 items from a set of 10 items.

Front

What is a sequence?

Back

An ordered list of numbers that follow a particular pattern or rule.

Front

What is a series?

Back

The sum of the terms of a sequence.

Front

What is the difference between a sequence and a series?

Back

A sequence is a list of numbers, while a series is the sum of those numbers.

Front

What is the formula for the sum of the first \( n \) terms of an arithmetic series?

Back

The formula is \( S_n = \frac{n}{2} (a + l) \) where \( a \) is the first term, \( l \) is the last term, and \( n \) is the number of terms.

Front

What is the formula for the sum of the first \( n \) terms of a geometric series?

Back

The formula is \( S_n = a \frac{1 - r^n}{1 - r} \) for \( r \neq 1 \), where \( a \) is the first term and \( r \) is the common ratio.

Front

What is a geometric series?

Back

A series 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 common ratio in a geometric series?

Back

The factor by which each term in the series is multiplied to get the next term.