Sequences Lecture Review

Flashcards covering key concepts and formulas for arithmetic and geometric sequences from the lecture notes.

What is the defining characteristic of an arithmetic sequence?

Each term after the first is obtained by adding a constant value, called the common difference, to the preceding term.

What symbol is typically used to represent the common difference in an arithmetic sequence?

d

How are the terms of an arithmetic sequence generally represented, starting with the first term 'a' and common difference 'd'?

a, a+d, a+2d, a+3d, …

What is the formula for finding the nth term (an) of an arithmetic sequence given the first term (a1) and the common difference (d)?

an = a1 + (n-1)d

What is the common formula used to find the sum (S_n) of the first 'n' terms of an arithmetic sequence?

Sn = n/2 * (a1 + an), where a1 is the first term and a_n is the last term.

What is the defining characteristic of a geometric sequence?

Each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

What symbol is typically used to represent the common ratio in a geometric sequence?

r