Sequences and Series

Front

What is a sequence?

Back

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

Front

What is a series?

Back

A series is the sum of the terms of a sequence.

Front

What is a geometric sequence?

Back

A geometric sequence is 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

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

Back

S_n = a(1 - r^n) / (1 - r), where a is the first term and r is the common ratio.

Front

How do you find the nth term of a geometric sequence?

Back

The nth term can be found using the formula a_n = a * r^(n-1), where a is the first term and r is the common ratio.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in the sequence.

Front

What is 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 found using the formula a_n = a + (n-1)d, where a is the first term and d is the common difference.

Front

What is the sum of an arithmetic series?

Back

The sum of the first n terms of an arithmetic series can be calculated using S_n = n/2 * (a + l), where a is the first term, l is the last term, and n is the number of terms.

Front

How do you find the first few terms of a geometric sequence?

Back

Start with the first term and repeatedly multiply by the common ratio to find subsequent terms.