Algebra 2 Sequences and Series

Front

What is the Explicit Arithmetic Formula?

Back

a_n = a_1 + (n - 1) * d

Front

What does it mean for a series to diverge?

Back

A series diverges if the sum does not approach a finite limit as more terms are added.

Front

What is the sum of the series written in Sigma Notation: Σ from k=1 to n of k?

Back

The sum is given by the formula S_n = n(n + 1)/2.

Front

What is the Finite Geometric Series Formula?

Back

S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.

Front

How do you find S_n for an arithmetic series?

Back

S_n = n/2 * (a_1 + a_n) or S_n = n/2 * (2a_1 + (n - 1)d).

Front

What is the difference between an arithmetic series and a geometric series?

Back

An arithmetic series has a constant difference between terms, while a geometric series has a constant ratio.

Front

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

Back

a_n = a_1 * r^(n - 1).

Front

What is the significance of the common ratio in a geometric series?

Back

The common ratio determines how each term is related to the previous term.

Front

What does it mean for a series to converge?

Back

A series converges if the sum approaches a finite limit as more terms are added.

Front

What is the formula for the sum of an infinite geometric series?

Back

S = a_1 / (1 - r) for |r| < 1.